I used my first gen G4 mini for years as a media center and it had trouble playing anything other than standard definition .avi files. I couldn't use it for Netflix, Hulu or even YouTube, and there was no way it would play any high definition content. If you're planning on using it to rip and encode DVDs then it's going to be very slow. If you're planning on just making a disc image of each of your DVDs then and storing them on an external hard drive then that would be a bit faster and you'd probably be able to play them in VLC with no problems. (Not sure if the Apple DVD Player will load disc images.)
Do you happen to have an Xbox 360 or PS3? I'm currently using my mini as a media server, storing lots of TV shows and movies on an external drive and sharing them to my Xbox using an application called Playback. That way I can use my Xbox for just about anything I want to watch: downloads, Netflix, Hulu, YouTube. The best part about this set up is that even though my mini can't process HD video or Blu-Ray rips it has no problem streaming them to the Xbox.