I haven't tried Dignan's option, but I can already tell you that Hardbrake works great! It does exactly what I want.

I will encode to Xvid instead of H264 though, because my Freecom media player does not support H264. It plays virtually everything, except codecs with an Apple stamp, like H264 and MOV.

Now all that remains finding out is how I can rip the subtitles from the movie...