Personally, I like using vdub to cut up bigger source files, and for final audio muxing and encoding.
It's small, efficient, fast, and free (as in beer and speech) which is always a nice bonus.
This writeup on doom9.net really helped me out a LOT back in the day when I started using vdub, it goes over a lot of procedures you will most likely be doing a lot of.
Doom9.net - The Definitive DVD Backup Resource
And something I really didn't see stressed here...
Don't work with compressed source material unless you absolutely have to.
If you do rip your clips from a dvd, dump the vobs, and if you have to (as in, your editor of choice needs avi input, for example) use something like vdub to make it into uncompressed avi.
It'll take a ton of drive space, but it's worth it in the end, because going through several rounds of lossy compression will make the end product look trashy.
Oh, and for audio, there's audacity, which is a great little audio editor, also open source,
and you can always go check out sites like
opsound: free love, free music and
Podsafe Audio - Podcast Music for the Revolution for free music that you can edit and play with all you want.