I want to install some version of Linux on my 1st gen Apple TV.
What Linux variants can be installed on an Apple TV?
Bonus points: is this even a good idea? How useful is the Apple TV as a computer? Do you have a link to detailed tech specs?
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.
OpenElec 2.0 is made for ATV v1 and 2 and supports the newer HD encoder you can install.
If you have an apple tv it works very well with openelec 3, even better with a Broadcom BCM970012 or BCM970015 Crystal HD card fitted, but this way you lose the wireless network unless you add wireless usb, wich is well supported i openelec. I have RPi also and prefer the ATV as dedicated openelec media server and the RPi as my little linux box, which is no surprise as the ATV was designed as a media server and the RPi as lovely little computer :-) but I do keep a dedicated 16gb openelec SD card for the RPi for when I am on the move. Considering I bought my ATV over 5 years ago, the Linux, XBMC, openelec solution has kept the ATV from being consigned to the scrap heap long ago, to the point of it being now, as good as the RPi and maybe better in some cases and is a far better solution than some of those media playes sold today.
Short answer now you have the RPi, install openelec 3 on the ATV for media centre fun and use the RPi for good old Linux fun, with GPIO and all the goodies it was designed with :-)