Two different questions.
1. AppleTV can read videos you've put in iTunes, which means they've been converted to the formats iTunes accepts (read: MP4). It's easy to convert videos to MP4 format if they're not already that way; I use a program called VisualHub (which has been discontinued) but there's another called Redux Encoder that works fine and is also free. It works on batches so I can just dump a bunch of videos in there, go to bed, and in the morning they're all converted and put into iTunes, ready for streaming.
2. There are two ways to approach the topic of AVI to DVD. One is to convert them to DVD images, Redux Encoder can do that, as can toast (Toast does a very nice job, even combining multiple videos into a single, menu'd DVD).
The other (lazy man's) way is to buy a DVD player that can read DivX/XviD AVI files off a "data" (ISO) DVD. So no converting needed, you just drag the files onto a blank disc, burn, stick in the dvd player. Done. No fancy menus, but basic navigation is provided.