Sound, sound, sound, sound, sound. The biggest issue with musical self tapes is SOUND. You can use a lavalier microphone and it wouldn't hurt to have one anyway, but I've found that this doesn't actually fix the bigger issue with sound which is bounce. So how do we keep the sound from bouncing all over our room? Remember this little tidbit: you want the light in front of you and the sound control behind you. Think soft and dense like a sound board, or a blanket. I use a soft chair. I'm quite small so this works for me because even standing the chair back is the height of most of my body. The chair is thick and soft.
So what can we put behind us?
1. A blanket or comforter. Tack it or nail it to the wall so that it is high enough to be behind your head and so the camera doesn't see where it ends.
2. Soft furniture. This mostly is going to work if you can stand a couple of feet in front of the furniture. Some of my students use a mattress for this and then drape a blanket over it.
3. Books. When I tape at my sister's I use her bookshelf to tape against. It's pretty, it's vague enough not to distract the eye and it deadens the sound so there is no bounce.
4. Sound boards or acoustic panels. Do a quick search of acoustic panels and you'll see they aren't really that expensive. Buy one in blue, if that's how you tape yourself. Or any color you use for your non-music work. You can hang it on the wall like art and leave it there. You can go all out and hang some over the entire wall. Its not a necessary purchase but if you feel you'll be self taping a lot it couldn't hurt.
Figuring out the sound in a space takes some time. Do several tapes where you check the sound of you singing and the sound of your instrument.