What is a good path for a Servlet?

WHen using paths - (which is a valid SLing way- https://sling.apache.org/documentation/the-sling-engine/servlets.html) - you can invoke the Servlet without accessing a JCR node.

That is - you can use an AJAX request or write HTTP GET/POSTs. All of these are accomplished without accesing a JCR node. So when you want to invoke a servlet from outside of AEM (a web client or desktop app that does not access a JCR node or using an AJAX request) - binding by path is the way to do it. 

Here is an example of a path - under bin - and an AJAX call invoking the servlet:

$('#submit').click(function() {
    var failure = function(err) {
             alert("Unable to retrive data "+err);
   };
  
    //Get the user-defined values that represent claim data to persist in the Adobe CQ JCR
    var myFirst= $('#FirstName').val() ; 
    var myLast= $('#LastName').val() ; 
    var date= $('#DateId').val() ; 
    var cat= $('#Cat_Id').val() ; 
    var state= $('#State_Id').val() ; 
    var details= $('#Explain').val() ; 
    var city= $('#City').val() ; 
    var address= $('#Address').val() ; 
    var claimId = createUUID(); 
  
  
    //Use JQuery AJAX request to post data to a Sling Servlet
    $.ajax({
         type: 'POST',    
         url:'/bin/mySearchServlet',
         data:'id='+ claimId+'&firstName='+ myFirst+'&lastName='+ myLast+'&address='+ address+'&cat='+ cat+'&state='+ state+'&details='+ details+'&date='+ date+'&city='+ city,
         success: function(msg){
 
           var json = jQuery.parseJSON(msg); 
            var msgId=   json.id;
            var lastName = json.lastname;
            var firstName = json.firstname;
              
            $('#ClaimNum').val(msgId); 
            $('#json').val("Filed by " + firstName + " " + lastName);   
         }
     });
  });

In Dispatcher - you can allow access to this path. See:

https://docs.adobe.com/docs/en/cq/5-6-1/deploying/security_checklist.html

That way - AJAX requests will work