Best PHP handler for cPanel on CentOS
After that, probably FCGI if you want to get rid of the mentioned "problems" (in quotes because it depends on your environment if these are problems at all).
Here's a very good comparison between the handlers:
One interesting option (that I have no experience of) is running DSO with mod_ruid2 which gets rid of the "permission problems" with DSO.
But as it says on its page, there are some security issues related to that (although, it would require Apache itself to be vulnerable which is of course possible).