A good smartphone will provide better resolution than most webcams. You should get something that does 1080p with a 16:9 resolution (1920x1080). Low light capability is important for home videos, and the big thing is lighting and camera angle. Whatever camera you get, if you have is aiming up your nose and the room is dark, it's not going to matter how good the audio is.
Your answer left a lot of details out, like what kind of videos, whether you'll be processing the audio and video separately and syncing, what software you'll be using, etc.
If you are trying to set up so you can record the audio directly into the video capture, that can make things harder IME.