There are really many php Ajax frameworks, some of them listed here, and really hard to choose the best one. As for me, I prefer simple and tiny Mini Ajax library for simple tasks.
I like Sajax Framework. It's easy to understand and cool. http://www.modernmethod.com/sajax/ Wish you good luck with AJAX.
I've only used two... started with SAJAX, mentioned above, but moved to XAJAX ( xajaxproject.org ) I'm happy with it. With SAJAX you had to essentially write twice as many functions, the PHP function would have to call a javascript function. XAJAX simplified things by automating the javascript side of things, so the hard work is all done in PHP. -Ryan