Stealth - You can do this directly with Avidemux - from the DVD in the drive. Open the DVD on the Desktop. From there open it in Avidemux.
Make a directory to put the Audio in. Go to > Audio > Save - or just Ctrl + Alt > S. In the dialog that opens, go to the directory you made, type a name - Vidmusic.ac3 (etc) - and OK.
In a couple of minutes you'll have the AC3 (or other) - file in the directory.
Close Avidemux and remove the DVD from the drive.
Convert the AC3 file to WAV with SoundKonverter.
Do the conversion to WAV - so that you have a lossless format to work with.
Open the WAV file in Audacity. Most of a DVD's track you won't want - just the music you prefer. Select each piece you want - and a little more at each end... (A bit extra trims easily - cut off short, you'll need to re-do it.)
When you have all the pieces you need, close Audacity with the WAV file (or save it as backup in FLAC.)
Open each of your pieces in Audacity - spread the waveform out, so you can see the exact starts-finishes to trim to. Leave a small amount - say 3-5 seconds - each end, and use those as your fade-in and fade-out from and to silence.
If that's not clear, Post back, and we can go through it by steps... Not everyone is familiar with Avidemux and Audacity.