I’m a music teacher (private) and producer/engineer. I’m actually in the midst of shooting a number of workshops and teaching video for distribution right now. What you’re looking to do can range from very simple to very complex.
Are you trying to use this to teach your friends parts? or just share your performance. I’m assuming the latter.
Best low cost solution is to use your webcam with built-in mic. But you have little control of the video angle and the audio might be noisy or muffled.
Any smartphone that can shoot HD, or any small consumer camera that can do the same is sufficient for the video. The key is angle and lighting. If you have decent fill lighting in the room - that doesn’t cast shadows and is even throughout, you might try a floodlight or worklight, focused on you, but a ways back. If it doesn’t get too hot, you can mask or tint the light with a gel (cheap online) or a thin t-shirt. When I’ve done improv lighting in the past, I’ve slightly dampened (not dripping) the t-shirt and used a light pastel color to improve the light quality.
Regardless, good lighting is critical. As for placement, if possible I’d go for two cameras. One on a tripod (even a little mini one for travel) with a medium shot of you and the guitar, with a second one framed tighter to your face/hands and at a different angle. Better yet, have it on a tripod and someone else switch shots between medium and closeups of your hands, face, guitar.
For the audio, if you can, I’d recommend a small digital stereo recorder like this. Cheap, sound quality is great and you can select file format and sample rate/bit depth. It uses microSD cards and also can connect via USB. There’s lots of models like this out there, but this one is probably the best for cost/quality ratio. In my studio, we have 4 of these for quick remote recording, foley and environmental recording and never had a problem.
Once you’ve got a good set of video and audio, time to hit the computer. We use Pro Tools and Final Cut Pro, but I’m assuming you’re going for some more consumer based solution. On Windows, Movie Maker is free and on Mac, iMovie. For the audio, try Audacity or on mac, garageband (included in the OS) if you need to clean it up, but you can probably just import the audio right into the video editor You might need to fiddle a bit aligning the sound to picture (not sure if those programs are frame accurate) but one good trick is to make a loud, sharp noise - that will be a useful reference point to alignment. It needs to be sharp and quick to match the transient of the audio to the visual easily.
Any questions, feel free…