You have several options that I can think of:
Remington 870 Express or Express Magnum
Mossberg 500
Mossberg 535
Mossberg 835
Maverick 88
H&R Pump Action (Toronto Bass Pro has them on sale for $199.99)
Possibly a Norinco HP9 (870 Clone), if they come with choke tubes.
The Express Magnum, Mossberg 535 and 835 can handle 3.5" shells that might come in handy for some goose and turkey applications. I believe that the Mossberg 500 and 535 combos also come with three choke tubes, as opposed to the single modified tube that comes with the Express and Mossberg 835 shotguns. The 535 combo with 28" VR barrel, three chokes and a rifled barrel with sights is probably the most economical way to equip a new hunter for most types of game.
I am not very familiar with the P350, though I've also heard that they are derived from a Benelli design. Not knowing much more, I'd look at factors such as the number of choke tubes that come with the gun, whether it can shoot 3.5" shells, how it fits you and whether you prefer the synthetic over a wood stock.
Best of Luck,
Frank