I recently bought a 1920 Fulton 12 ga double for $275. You guys are making me realise how lucky I was.
If you want really cheap, a used H & R / NEF can be had for well under $100.
My Uncle Paul used an old Topper single barrel 16 ga for hunting everything for most of his adult life, but he really knew that gun and could hit whatever he saw. He used it so much he wore all the blue off it, but he could just walk out his kitchen door and hunt. Different place and time now.
You may want to look at a used Mossberg 500, probably available for $175, or a used Winchester 1200 for $250 or so. Some older "store brand" guns are out there, Sears, J C Higgens, Wards, etc, and these are Stevens, High Standard, Winchester, etc guns with less expensive wood for much less money than the "name" brands.
Shotguns require practice and knowledge of how you and your individual gun shoot. You must spend some time and a few boxes of shells practicing and patterning the gun if you actually intend to hit anything moving with it. Sorry to be so long winded.
Enjoy whatever you finally select and good luck.
Mark