Generally speaking, for this kind of operation, a post back (which is really not what it is, you are simply navigating back to the same page, and I assume that the items are part of a GET operation, so there is no "post) is what you don't want.
The reason for this is because your URL structure becomes sloppy. If I wanted to bookmark the search results, how would I go about doing so? I can't, because you decided to download massive amounts of content through AJAX.
As a general rule of thumb, if you are downloading large amounts of content into your browser, you should generally have a URL for that, as it's a resource in itself.
As for maintaining state, if you want to do that without rewriting the URL (in other words, when they go to "/search", you want the previous results) you can either store the form fields in a cookie and populate it from the cookie, or the values in the URL, or use a database of some kind to store the preferences.
Basically, every time someone submits values to that page, you would write them to the data store (cookies, files, database, whatever). Otherwise, if on that page, you retrieve them from the store using whatever it is you are using to identify the current user.