I would definitely get one that does at least 1080p. If you want good performance, make sure it also does at least 60 frames per second (you can always drop it to 30 or 24 in post). I don't know what's latest and greatest, but I have a Logitech c922 that I got about 5 years ago. Taking a quick look, they are about $60-$70 now (used to be $120). Also, cameras on the latest phones are quite good.
What you really need (if you don't have one already) is a good front light source like a light ring. Webcams especially need a good light source, and the difference is night and day. I got one on Amazon about the same time for $80.
If you don't have a good mic, I recommend the Blue Yeti. This has been a standard, and is what I use to do all my voiceovers. If you've just been using a PC mic, this will also provide a HUGE leap in quality. They are about $90 now, and provide probably the most bang for the buck.