Having been through this the hard way, I would avoid cheap single shot guns. Buy something with a future. Pumps and autos have the advantage of being able to be loaded one shot at a time, yet retain usefulness as the shooter matures, and can be had with youth stocks which are exchangeable with full size stocks later. If size is an issue bear in mind that Length of pull is relative, 14" in a double gun is much shorter than 14" in a pump or auto, and is easier to handle due to the shorter action length, distance to the fore end and overall shorter dimensions. Probably a 20 ga. unless a stout youth, but you can by low recoil 12 ga. loads to start with and practice on targets. Starting out with the nicer quality guns which your shooter can continue on with will be much more satisfying, and the better fit and finish, particularily the smoothness of the action, safety, and stock design will be worth it. I have shot some youth starter guns which have a comb like a razor blade, and made me dread the trigger pull in a twenty gauge! Imagine the effect on a beginner! Specifics which were excellent for us, Remington 870 pumps, 1187 autoloaders, in 20 ga. Ithaca doubles, in 20 ga. But I would think any of the light doubles or o/u's in a 20 would work. We have an assortment of those, none over 6#'s loaded. 12's will need to be heavier, or lightly loaded to avoid discouragement from recoil. Felt recoil is unpredictable. I have twin girls 14 within an inch and pound of each other, between 5'-5'1, 85#'s. Small to say the least, yet one is recoil sensitive, one will touch off shot after shot with 12 ga. golden pheasant 1 3/8ths high brass in a 6.25# doublegun and never blink.