What's the minimum needed to make a video of my guitar performance with good quality sound?
There are a couple ways you could go about this.  If you can do it in a single take, then you can record the audio and video at the same time and then simply sync them up and all will be well in the world.

If you want to be able to do multiple takes, then what you should do is do it the way they make music videos.  Do the audio first, make your recording and do your editing and multiple takes.  Once you have done that, play back the audio aloud and fake it.  You don't actually use the audio from while playing in the video, you just record yourself playing in sync with the pre-recorded audio.  After, you do the same sync process as you would have done with the first option.