• Incorporate a VF Page into the Case Object where Users could upload a single image
• Have that single image stored as an Attachment for that Case
• Renaming that Attachment 'CasePhoto1.jpg'
• Extract that Attachment's ID and insert it into a custom field named CasePhoto1ID__c

public with sharing class CasePhotoUploadController1 {

    Private Static FINAL String fixedFileName = 'CasePhoto1.jpg';

    public boolean displaying { get; set; }
    public Case pageCase;
    public Blob casePicFile { get; set; }
    public Id currentPicture { get; set; }
    
    /** Constructor, grab record, and check/load an existing photo */
    public CasePhotoUploadController1(ApexPages.StandardController controller) {
        pageCase = (Case)controller.getRecord();
        
        List<attachment> currentPictures = [SELECT Id FROM Attachment WHERE parentId = :pageCase.Id AND name = :fixedFileName LIMIT 1];
        if(currentPictures.size() != 0) {
            currentPicture = currentPictures.get(0).Id;
        }
        
        displaying = true;
    }

    /** toggle switches between the photo display and photo upload form */
    public void toggle() {
        displaying = !displaying;
    }
    
    /** saveFile clears any existing (secondary) Case picture, retrieves the data from the form, and saves it under the relevant filename*/
    Public Pagereference saveFile() {

        // first, we cannot have any conflicting files
        List<attachment> savedPicture = [SELECT Id, name, body FROM Attachment WHERE parentId = :pageCase.Id AND name = :fixedFileName];
        if(savedPicture.size() > 0) {
            delete savedPicture;
        }
       
        // Now, the new blob is saved
        Attachment a = new Attachment(parentId = pageCase.Id, name = fixedFileName, body = casePicFile);
        insert a;
        
        currentPicture = a.Id;
        
        displaying = true;
        return null;
    }
  }

<apex:page standardController="Case" extensions="CasePhotoUploadController1" showHeader="false" standardStyleSheets="true" sidebar="false">

<apex:form id="contentForm">
<div style="height:170px;">
    <apex:pageBlock mode="edit">
    
        <apex:pageblocksection columns="1" rendered="{!displaying}">
            <apex:image height="150" value="{!URLFOR($Action.Attachment.Download, currentPicture)}" rendered="{!currentPicture != null}"/>
            <apex:outputPanel rendered="{!currentPicture == null}"><em>No picture currently available</em></apex:outputPanel>
        </apex:pageblocksection>
        
        <apex:pageblocksection columns="1" rendered="{! !displaying}">
            <p>Use the button to below to select a new file and then press "Save"</p>
            <apex:inputFile value="{!profilePicFile}" />
            <p>Or press Cancel to return.</p>
        </apex:pageBlockSection>
        
    </apex:pageBlock>
</div>
    <apex:commandButton value="Upload new photo" action="{!toggle}" rerender="contentForm" rendered="{!displaying && currentPicture!=null}"/>
    <apex:commandButton value="Upload photo" action="{!toggle}" rerender="contentForm" rendered="{!displaying && currentPicture==null}"/>
    <apex:commandButton value="Cancel" action="{!toggle}" rendered="{! !displaying}"/>
    <apex:commandButton value="Save" action="{!saveFile}" rendered="{! !displaying}"/>
</apex:form>
  
</apex:page>