Of course the other thing to remember is that in Trap and Skeet, you are probably going to go out and shoot at least a couple of rounds of 25 birds each, and its pretty typical to shoot at least a hundred shells. Field guns are designed for hunting where if you shoot a box of shells in a day, that's a lot.
The point is, you want something with a decent recoil pad, and more weight than you would want if you were carrying the gun in the field all day. A light weight gun with a plastic recoil pad will beat you up in Trap or Skeet. If you want a light weight gun, go with a Semi Auto, they will give you less felt recoil, and some like the Benelli have a decent recoil reduction system.
If it were me looking for a gun in your price range, I'd go for a used Citori with screw in chokes.