I have two problems here -
1. When invoking Save, the value of Input Text of "Broadcast Number" is not getting sent to the controller, without removing the <apex:selectList>
2. When click on Next / Previous Page (in pagination); the values are getting reset

VF Page

<apex:page standardController="Commercial__c" extensions="CommercialSchedulerVFPController">

    <apex:form id="myform">
        <apex:sectionHeader subtitle="{!titleValue}" title="Commercial Scheduler"/>
    
        <!-- Commercial Details Section -->     
        <apex:pageBlock id="detailsBlock" title="Commercial Details">
            <apex:pagemessages />
            <apex:pageBlockButtons location="top">
                    <apex:commandButton action="{!save}" value="Save"/>
                    <apex:commandButton action="{!doCancel}" value="Cancel" immediate="true"/> 
            </apex:pageBlockButtons>
        
            <apex:pageBlockSection title="Commercial Details"  columns="2">
                <apex:inputField value="{!commercialObj.Name}" required="true"/>
                <apex:inputField value="{!commercialObj.Running_Time_Seconds__c}" required="true"/>
                <apex:inputField value="{!commercialObj.Account__c}"/>
                <apex:inputField value="{!commercialObj.Contracted_Broadcast_Time_Seconds__c}" required="true"/>
                <apex:inputField value="{!commercialObj.Broadcast_Start_Date__c}" required="true"/>
                <apex:outputField value="{!commercialObj.Total_Broadcast_Time_Seconds__c}"/>
                <apex:inputField value="{!commercialObj.Broadcast_Stop_Date__c}" required="true"/>
                <apex:outputField value="{!commercialObj.Broadcasts_Scheduled__c}"/>
            </apex:pageBlockSection>
        
    
        <!-- Broadcast Chart Section -->        
           <apex:pageBlockSection title="Broadcast Chart"  columns="1">
            <apex:chart name="AnnualRecurringRevenue"
                                data="{!TimeSlotResults}"
                                width="100%" height="200"
                                >

                          <apex:axis type="Numeric" position="left" grid="true"                              
                                   title="Seconds" 
                                   fields="broadcastNumber"
                                   steps="10">
                            <apex:chartLabel />
                        </apex:axis>

                        <apex:axis type="Category" position="bottom" grid="false"
                                   title="Date"
                                   fields="broadcastNumber">
                            <apex:chartLabel />
                        </apex:axis>

                        <apex:barSeries orientation="vertical" axis="left" stacked="false"
                                        xField="broadcastNumber"
                                        yField="broadcastNumber">
                            
                        </apex:barSeries>
                    </apex:chart>
            
            </apex:pageBlockSection>
        
        <!-- Timeslots Section -->  
            <apex:pageBlockSection id="pbTimeslot" title="Timeslots" columns="1">
                 <apex:selectList id="selectId" value="{!programGenreValue}" size="1">
                  <apex:actionSupport event="onchange" action="{!getResults}" />  rerender="pbTimeslot,detailsBlock" 
                  <apex:selectOptions value="{!programGenre}"/> 
                </apex:selectList>
           
                <apex:pageBlockTable id="maintable" value="{!timeSlotResults}" var="t" rendered="{!NOT(ISNULL(timeSlotResults))}" width="100%">
                    <apex:column width="20%"  headerValue="Number of Broadcasts">
                        <apex:outputPanel styleClass="requiredInput" layout="block">
                        <apex:outputPanel styleClass="requiredBlock" layout="block"/>
                            <apex:inputText value="{!t.broadcastNumber}" style="width:50px"/>
                        </apex:outputPanel> 
                    </apex:column>
                    <apex:column width="20%"  headerValue="Program Name">
                        <apex:outputLink value="/{!t.timeSlotObj.Id}" target="_blank">
                        <apex:outputText value="{!t.timeSlotObj.Program_Name__c}">
                        </apex:outputText>
                        </apex:outputLink>
                    </apex:column>
                    
                    <apex:column width="20%" value="{!t.timeSlotObj.Program_Genre__c}" headerValue="Program Genre"/>
                    <apex:column width="20%" value="{!t.timeSlotObj.Timeslot_Date_Time__c}" headerValue="Timeslot Date/Time"/>
                    <apex:column width="20%" value="{!t.timeSlotObj.Remaining_Commercial_Time_Seconds__c}" headerValue="Remaining Commercial Time (Seconds)"/>
                </apex:pageBlockTable>
            
                 <apex:outputPanel >
                     <div align="center">
                    <apex:commandButton disabled="{!!hasprevious}" action="{!First}" value="|< First" immediate="true"/>&nbsp;&nbsp;&nbsp;&nbsp;
                    <apex:commandButton disabled="{!!hasprevious}" action="{!Previous}" value="Previous" immediate="true"/>&nbsp;&nbsp;&nbsp;&nbsp;
                   <apex:outputText >{!IF((pageNumber * size)>noOfRecords, noOfRecords,(pageNumber * size))} of {!noOfRecords}</apex:outputText>&nbsp;&nbsp;&nbsp;&nbsp;
                    <apex:commandButton disabled="{!!hasnext}" action="{!Next}" value="Next" immediate="true"/>&nbsp;&nbsp;&nbsp;&nbsp;
                    <apex:commandButton disabled="{!!hasnext}" action="{!Last}" value="Last >|" immediate="true"/>   
                    </div>
                 </apex:outputPanel>
             
             </apex:pageBlockSection>    
        
        </apex:pageBlock>   
            
    </apex:form> 

</apex:page>

Class

public class CommercialSchedulerVFPController{

    public Commercial__c commercialObj	{get;set;}
    public Integer noOfRecords			{get; set;}
    public Integer noOfBroadcasts 		{get;set;}
    public String programGenreValue 	{get;set;}
    public ApexPages.StandardSetController con{get;set;}
	public DateTime startDate;
    public DateTime endDate;  
    public Integer size {get;set;}
    public String commercialObjId		{get;set;}
    public String titleValue 			{get;set;}

	List<TimeSlotWrapper> timeSlotResults  {get;set;} 

//  Standard Constructor    
    public CommercialSchedulerVFPController(ApexPages.StandardController controller){
       this.commercialObj 	= (Commercial__c)controller.getRecord();
       
       commercialObjId = ApexPages.currentPage().getParameters().get('id');
       programGenreValue 	= '';
       size = 5; 
       if(commercialObjId == Null || commercialObjId == ''){
        // Represents a New Page 
           commercialObj 		= New Commercial__c();
           titleValue			= 'New Commercial';
           
           initStdSetController();
        }
        else{
        //	 Represents an existing Edit Page	
             commercialObj 			= [SELECT Id,Name,Running_Time_Seconds__c,Account__c,Contracted_Broadcast_Time_Seconds__c,Broadcast_Start_Date__c,Total_Broadcast_Time_Seconds__c,Broadcast_Stop_Date__c,Broadcasts_Scheduled__c 
             					 		  FROM Commercial__c 
             					  		  WHERE id=:commercialObjId
             					   		];
             titleValue			 		= commercialObj.Name;
             Map<Id,Double> timeSlotBroadcastNoMap = fetchExistingTimeslotValue();					   
             initStdSetController();					               
        } 
       
    }

	public void initStdSetController(){
        
  //	Change these dates to actuals      
        startDate 		= Date.today();
        endDate 		= Date.today()+14;
        
        con 			= new ApexPages.StandardSetController(Database.getQueryLocator(getQuery()));
        con.setPageSize(size);
        noOfRecords 	= con.getResultSize();
    }
    
 //	Method to do a dynamic query based on the selected Genre
 private String getQuery(){
        
        //	Change these dates to actuals      
        startDate 		= Date.today();
        endDate 		= Date.today()+14;
        
 			String query = 'SELECT Timeslot_Date_Time__c, Remaining_Commercial_Time_Seconds__c, Program_Name__c, Program_Genre__c'
 			 			 + ' FROM Timeslot__c';
                        // + ' WHERE Timeslot_Date_Time__c >=:Startdate and Timeslot_Date_Time__c <=:Enddate';               																	
                    
            system.debug('@@ programGenreValue @@'+programGenreValue);        	 
        	if(programGenreValue!='' && programGenreValue!='All'){
        		query	+= ' WHERE Program_Genre__c =: programGenreValue '; 
        	}
        
        System.debug('@@ query @@ '+query); 
        return query;
    }
    
  
//	This method is used to invoke the list from the VF Page    
    public pageReference getResults(){
    	system.debug('@@ getResults - Start @@');
    	initStdSetController();
    	system.debug('@@ getResults - End @@');
    	return null;
    }    
    
  // Methods used for pagination logic
  public Boolean hasNext {
        get {
            return con.getHasNext();
        }
        set;
    }

    // indicates whether there are more records before the current page set.
    public Boolean hasPrevious {
        get {
            return con.getHasPrevious();
        }
        set;
    }

    // returns the page number of the current page set
    public Integer pageNumber {
        get {
            return con.getPageNumber();
        }
        set;
    }

    // returns the first page of records
     public void first() {
         con.first();
     }

     // returns the last page of records
     public void last() {
         con.last();
     }

     // returns the previous page of records
     public void previous() {
         con.previous();
     }

     // returns the next page of records
     public void next() {
         system.debug('@@ con @@'+con);
         for (TimeSlotWrapper loopvar : timeSlotResults) {
         	system.debug('@@ timeSlotResults-loopvar @@'+loopvar);
         }
         con.next();
     }

     // returns the PageReference of the original page, if known, or the home page.
     public void cancel() {
         con.cancel();
     }
 
 //	This method will Cancel the transaction and redirect to the Object Page without validations    
     public Pagereference doCancel(){
        Schema.Describesobjectresult result = Schema.Sobjecttype.Commercial__c; 
        ApexPages.Pagereference cancelPg = new PageReference('/' + result.getKeyPrefix() + '/o');
        cancelPg .setRedirect(true);
        return cancelPg ;
    }
     
 
 //	This method constructs the picklist of Program Genre used for filtering the table     
    public List<SelectOption> getProgramGenre(){
        List<SelectOption> options                  = new List<SelectOption>();
        Schema.DescribeFieldResult fieldResult      = Timeslot__c.Program_Genre__c.getDescribe();
        List<Schema.PicklistEntry> ple              = fieldResult.getPicklistValues();
        
        options.add(new SelectOption('All','All'));

// 		Reading from the object definition to allow dynamic values to be added later        
        for(Schema.PicklistEntry f : ple){
              options.add(new SelectOption(f.getLabel(), f.getValue()));
        }       
        system.debug('@@ options @@'+options);
        return options;
    }
    
//	Fetch existing value of Timeslots for existing 
	public Map<Id,Double> fetchExistingTimeslotValue(){
		system.debug('@@ fetchExistingTimeslotValue - Start @@');
		
		Map<Id,Double> timeSlotBroadcastNoMap			= new Map<Id,Double>();
		List<Commercial_Slot__c> commercialSlotList 	= [SELECT Timeslot__c, Number_of_Broadcasts__c, Commercial__c 
															FROM Commercial_Slot__c 
															WHERE Commercial__c =: commercialObj.Id
															];
		
		
		for(Commercial_Slot__c loopvar: commercialSlotList){
			timeSlotBroadcastNoMap.put(loopvar.Timeslot__c, loopvar.Number_of_Broadcasts__c);
		}
		
		system.debug('@@ timeSlotBroadcastNoMap @@'+timeSlotBroadcastNoMap);
		system.debug('@@ fetchExistingTimeslotValue - End @@');
		return timeSlotBroadcastNoMap;
	}


//	Invokes the Save operation    
    public PageReference save(){
        system.debug('@@ save - Start @@');
        for (TimeSlotWrapper loopvar : timeSlotResults) {
        	
        	system.debug('@@ loopvar @@'+loopvar);
        	//if (cw.checked)
            //    selectedContacts.add(new ContactListWrapper(cw.serviceContractNotificationObj));
            //else
            //    unselectedContacts.add(new ContactListWrapper(cw.serviceContractNotificationObj));   
         }
        
        
        system.debug('@@ save - End @@');
        return null;
    } 
    

// This is to capture which numbers were entered i.e. changed the default from 0 to something else
    public List<TimeSlotWrapper> changedTimeSlotRecords {
        get {
            if (changedTimeSlotRecords == null) changedTimeSlotRecords = new List<TimeSlotWrapper>();
            return changedTimeSlotRecords;
        }
        set;
    }
    
     
	 public List<TimeSlotWrapper> getTimeSlotResults() {
        timeSlotResults 		= new List<TimeSlotWrapper>();
        
        for (Timeslot__c loopvar : (List<Timeslot__c>)con.getRecords()){
            timeSlotResults.add(new TimeSlotWrapper(loopvar));
        }
		system.debug('@@ timeSlotResults @@'+timeSlotResults);
        return timeSlotResults;
    } 
	 
	 // Wrapper Class to hold the Number of Broadcast Schedules
	 public class TimeSlotWrapper {
	
	    public Integer broadcastNumber {get; set;}
	    public Timeslot__c timeSlotObj { get; set;}
	
	    public TimeSlotWrapper(){
	        timeSlotObj 			= new Timeslot__c();
	        broadcastNumber			= 0;	
	    }
	
	    public TimeSlotWrapper(Timeslot__c t){
	        timeSlotObj 			= t;
	        broadcastNumber			= 0;
	    }   
	         
	 }  

}