There are several reasonably priced pump shotguns that could get you started for small game, deer, and casual target shooting.
The Mossberg 500, M535, M835, and Remington 870 Express are all available in combinations with 26 or 28" barrels with (modified tube for Remington and M835, or three chokes for M500 and M535) , plus a rifled shotgun barrel with sights.
The Maverick 88 (economy version of Mossberg) comes with a 28" barrel with modified choke tube. There's also a combination Mav 88 with 28" fixed modified and 18.5" cylinder choke, or an M500 combo with 28" barrel (3 chokes) and an 18.5" cylinder barrel.
Most of these shotguns are chambered 3", but you can get 3.5" chambers in the M535, M835 and Reminton 870 Express Magnum, which may come in handy for certain waterfowl/geese situations or turkey.
There's also a number of inexpensive short barrelled pump options, such as the Norinco HP9 (870 Clone) with 14" barrel and cylinder choke, or the Canada Ammo Dominion Arms Grizzly, which toutes a 12.5" barrel with modified Invector Choke. The latter also comes with ghost sights for an extra $10, which makes it a neat small game, deer and defence shotgun. The Maverick 88 and Mossberg 500 Persuader models are also available at reasonable cost, though like the HP9, they are essentially defence shotguns that can double for upland game unless you purchase a longer barrel with choke tubes.
All of these shotguns or combos are reasonably priced. Buying used could land a better quality shotgun for a reasonable price (i.e. if you could get a Remington 870 "Wingmaster" for little more than the price of a used "Express" model, I'd say go for it). A lot of older guns have fixed chokes though, and in the case of full choked guns are usually sub par for upland and don't usually pattern well with steel shot for waterfowl either.
There are a few good, inexpensive used doubles like the Stevens 311 that can occasionally be found at a reasonable cost (I got one about three years ago for $225 shipped to my door). Another general purpose shotgun might be a Savage 24 (12, 20 or .410 ga with .22LR or larger calibre), though finding used ones can be hit and miss, and they retain their value. I'd like to get an imporved cylinder and rifled choke tube (and maybe Red Dot sight) for my Savage 24F Combo, which comes in .22 hornet with a 12 ga barrel and modified choke tube, which would make it handy for all sorts of hunting scenarios. I got mine used for approximately $450, which is a bit cosltier than the other options discussed.
I hope that helps!
Cheers,
Frank