I think you probably mean an over under gun. This means that the you have two barrels mounted vertically on top of each other.

As opposed to a side by side, which is two barrels horizonally mounted next to each other. Or a semi automatic, which is a single barrel that has the ability to eject the first cartridge once used and automatically feed the next cartridge into the breech.

Which is probably good advice although lots of people use semi autos to great success. Plus semi autos tend to have very low recoil.

You best bet is probably to go to a good gun shop and ask to try the fit on a fews guns and see what fits you the best. You should also condsider a second hand gun as if they have been looked after that are probably as good as new. In that budget you would probably be looking at a Beretta or Browning.