I don't think there is any standard for a splash screen size. Personally, I do everything I can to avoid the need for one. If I'm doing so much initialization that the user might be concerned that the program hasn't started, then something is wrong with my design.

If you must, I'd keep it as unobtrusive as possible. Perhaps no more than 320x240 (in case you're users are like my Mom and still run in 640x480). As for centering, that's just arithmetic; do you not know how to calculate that?