OP, I think you need to work with an adult shooter to help you develop. Some of the other posters have mentioned, correctly, that low recoil, lower velocity shells will allow you to shoot the 12g comfortably. But, I fear they did not read your post. Thirteen years old, 5'7" and 95lbs. You're growing, but knowing kids in my own family, I don't think you're going to be able to shoot an 8 or 9lb 12g for very long on a saturday afternoon. The mechanics of trying to heave that gun to your shoulder are whats worrying me.
Not to mention there are no low recoil shells available to buy at this time.
Do a search on this forum for new/starting shooters and you'll see lots of information that may help you. I'd be in no rush to get into a 12g. I'm assuming you're shooting from 16yd line, hand traps, maybe some sporting clays with your buddies. At your age and size, I'd be focusing on lowest recoil possible so that you dont begin to develop bad habits. Think 28ga Remington 1100 or other auto loader. If you cant find 28ga or money is tight, then move to 20ga, same guns. Very last would be 12ga. Good luck.