I got a .410 NEF single shot for my son for his 11th birthday, and he loves it. Easy for him to clean and maintain by himself, and easy for him to handle in the field, being a bit lighter. So far, he's gotten squirrel, rabbits, and last year he knocked down his first pheasants with it.
We do just what you are talking about, using one of the stick-in-the-ground throwers, and he doesn't have any trouble hitting 15-20 out of 25 clays. He even went 22/25 with one box. We did notice with his that the shot group center hits a couple inches high at 15 yards, and slugs at 25 yards hit about 4" low, so I doubt he will ever do any hunting with slugs out of it.
All-in-all, he loves it. Being a break-open, it's very easy for him to clean, and that was one big thing for him - being able to do it all himself. One drawback is the price of the shells - usually in the $7-8 a box range. I'm going to get him one of the MEC Jr. reloaders (around $100) for Christmas this year, because he definitely shoots it enough. I've priced it out and the break-even point was 23 boxes of shells, which we'll definitely do in a year.
Good luck!
ETA: And if you do go with a 20 gauge, just look into getting a good recoil pad for the butt if you think it'll help.