We all live on a budget. If money is tight in your world, the mossburg pump is a hard gun to beat, due to their price in pawn shops...usually $125-$150 with 28" screw in choke barrels.
870's abound but command a much higher price.
The Remington 1100, 11-87 take a lot of recoil out of the equation on heavy 3" buck shot loads, and the Beretta 390-391 kick even less.
I have used a large number of shotguns over the years including the Ithaca 37, which will stomp your brains out and the Ithaca 10ga semi auto with a 32" full choke.
Some people have trouble with pumps, like me. I short stroke the action, ejecting the hull and leave an empty chamber...don't even ask me how I do this???
I still have two Mosburg pumps that are loaner guns that have seen a lot of hunting...they just keep working.
12ga, 3" #4 buck shot is awesome and if you can afford the T shot, buy it.