pt3d My 16 year old daughter is also just getting started in trap so I will share what I have learned over the last few months.
First for a shot gun, over unders are popular because they allow users to compete in doubles etc., for most beginners a single shot is fine and will allow them to compete in basic trap as well as handicapped. If using a double barrel the lower barrel is the correct one to use. A double does have a slight advantage in the weight department which as we all know helps reduce felt recoil, but that can be handled in other ways. Also there is a difference between a trap gun and a field gun, a trap gun is designed to shoot slightly higher than a field gun so you can keep the trap setting just above the aiming point, that way you never need to take your eyes of the trap. You will also find the comb is different between a trap and field gun as well as there are other slight differences which can be changed.
I found a slightly used Remington Spartan Sport (unfortunately these are no longer available new) series shotgun for my daughter for just over $200 it already had an adjustable comb installed (it is one of the points we adjust the gun to fit the shooter). I dropped another $150 getting the stock slightly shortened, an adjustable but plate, and a mercury weight (remember the weight issue from the over under) installed.
Now to what you want for a shotgun, I recommend getting a Trap model (in 12 gauge, it is needed for most competitions and the various teams usually require it) if you can find one you can afford, if not a field gun will work but some day she will want to upgrade. An over under is overkill for a new shooter, it will be a couple of years before she will be shooting doubles etc., for the same reason that the semi auto and pump trap guns are. None of these are bad guns but for someone just starting out there is a learning curve before they get to where they will need these things. By then they will be looking to upgrade anyway, and then they will have a better idea of what they need for what they want to shoot.
I don't have the card for the guy I used to set up my daughters shotgun up (he did the adjustable comb for the previous owner, and installed the adjustable butt and weight for me) but I will PM you with his info later, he is in Omaha. He is a trap and skeet shooter who gives great deals for kids getting started in the sport and will help get the shotgun adjusted so it fits her properly if you decide to go that route.
If you are in the Omaha area we can get together some day with our daughters to let them shoot a round and visit about the guns and what little I know at this point.