RE: turkey gun for a 13 year old?
You won't feel any recoil when you drop the hammer on a turkey.
I was shooting a 12 gauge when I was 11. I think if you get a 20 gauge now, you'll be ready for a 12 gauge by Christmas... I would get a 12 gauge. On turkeys the advantages are huge. Not saying a 20 can't do it, but I have yet to see a 20 gauge deliever more than a 60% pattern past 30 yards with a turkey load. I've shot lots and lots of them. They are 30 yard guns MAX.
I'd look for a good condition used Remington 1100, 1187, or a Beretta 390. I saw a few Berettas for sale in the local gun shop for under $450 in great shape.