I would not get a semi for trap. PITA you will regret.
I also would not get a bottom-loading pump like a BPS or M37, nice as they are. Trap usually requires you to keep the action open until it's your turn. With a conventional side-eject pump, you just drop a shell in the open action, wait for your turn with the gun on a toe tab or ground pad, and close it when you're ready to shoot.
Ultimately, you'll probably want a break-action, if it's specifically for trap. But a side-eject pump like an 870 or Model 12 is a good choice and almost equally convenient for the shooter.