ATI and Linux are fine, the proprietary drivers are a bit shoddy at times (though they've improved a lot as of late) but the free drivers are quite stable if rather poorly performing (unless you plan on gaming, this shouldn't matter).
Anyway, the hardware specs in your sig aren't very detailed - if some of your hardware is supported, it's most likely going to be your NIC or some other little device. However, most hardware is supported out of box, so I would suggest you simply try out a live CD and see if there are any problems.
As for "latest and greatest", well, that's all subjective. If you want all latest/bleeding edge software, Fedora would be a good distro but it's geared more towards advanced users and it ships with no proprietary drivers/software (except for some firmware) so if you want Flash, MP3 support or any of the likes be prepared to hop through some hoops. Mint and Ubuntu are usually the safe options for beginners with reasonably stable and up-to-date software and loads of proprietary stuff either coming with the installation by default or made easily available.
