It is not up to the distribution, any distribution can install the drivers. Of course it's easier if X is preinstalled, but that's the case with most distributions
it's really some work finding a distribution without X..they're quite minimal usually. Anyway, you can choose whichever distribution you want; if you want it work the easy way, pick up some newish one that handles packages in binary packages (Ubuntu, Fedora, SuSE, Mandriva etc. etc. etc. - any one of the big ones).
Installing drivers is done either trough the package manager of the distribution. That's the easiest way - point, click and restart X (or in some cases it's good to reboot the whole machine to make sure the new graphics driver module is inserted into the kernel correctly). Second best choice is to get the proprietary driver directly from the manufacturer site, extract the package, read the installation instructions included (usually README or INSTALL) and do as they say, often just run (as root) the installer executable.
Both ATI and nVidia cards work on Linux, both nicely, and both can cause trouble. Nowadays nVidia cards often feel to work better, so if you don't have any other criteria for the choice, go for nVidia. If you want ATI for some reason, go ahead, it's ok. But before buying the card, visit the manufacturer site and read their documentation
to find out, which card models work with their Linux drivers. After that's fine, buy the card, install it and start working with the drivers. Usually the 3d drivers themselves don't pose a big problem, the problems come after you try to install 3d desktop effects
