I waited until I was 14 to shave, but I hit puberty early, so I was a hairy kid. I didn't shave my mustache back then though, so it looks odd (to me at least - other people don't seem to think so). So, my advice to you is to shave everything when you start.
Also, about the thicker thing, I've heard this a lot, but if you shave every 2-3 weeks, it shouldn't be too bad I imagine (although, I do admit, I am not an expert in this particular sort of thing).