There are lots of possibilities and it's a while since I played with these things, so I don't know any more what is the best or easiest to use.
I had some success in the past with http://nvrec.sourceforge.net/
which may do all you want in one go.
Otherwise there are many other PVR type apps for linux. Just search for 'PVR' on http://freshmeat.net
. If you cannot capture directly to divx or mpeg4 two good toolkits for translating between formats are 'transcode' and 'mencoder'. The latter is the encoding partner of mplayer. You can find either by searching Freshmeat.
Edit: Now I stop to think about it, you may find that mencoder or transcode can be configured to do everything in a single step.