What Linux variants can be installed on an 1st generation Apple TV?
The first generation Apple TV had a pretty low powered Intel CPU, as you can see in the specs here. So in theory, you should be able to run just about any Linux distro, just a question of how much hacking you're willing to do.

There are a bunch of resources for doing this, but a good one is at the atv-bootloader project. There are tools to create a nice USB stick that should do most of the work for you.

As for how useful it is, don't expect much for general purpose computing - after all it's a 1 GHz Pentium-M with 256 MB of RAM. But it may do reasonably well for some home theatre tasks, or if you need a home automation server or similar box.