For practice and small game hunting I would suggest a 22 long rifle and/or a 20/12 ga shotgun. Or a combo would be really nice. They make over and under guns with a 20 ga barrel and a 22 rimfire. Or Rossi and some others make guns that you can swap barrels from one to the other.

I suggest looking at the Marlin model 60 semi auto, a Henry lever action or the Marlin and Savage bolt action rimfires. All should be in the low to sub $200 price range. And you can get single shot shotguns for around 100 bucks or so from Rossi and H&R/NEF. They tend to kick though because of the light weight. Or you could get a Mossberg 500 or Remington 870 for 250-300 dollars, they are pump shotguns. H&R also makes a pardner pump gun for under $200. I had one, pretty nice gun for the money. Nice fit and finish and pretty wood. The down side is it is made in China.

You could also look for a used gun, nothing wrong them if they were taken care of. You could probably get a decent used semi auto shotgun for what a new pump gun would cost if you looked around enough. I often see remington 1100's and others in the 3-4 hundred dollar price range. Heck I picked up a browning A-5 for 450 a few years ago.

My advise is if you want to plink and squirrel hunt, get a 22 rimfire. Fairly cheap and a blast to shoot. If you want to small game hunt, like bunnies, birds and squirrel it's hard to beat a 20 or 12 ga shotgun. And you can take them trap and skeet shooting as well which is a lot of fun. Stick with the 20 ga or 12 ga though. They are cheaper to shoot. .410, 28 and 16 ga shells are pretty expensive compared to the other two. Sometimes twice as much depending on what you are buying.

Just my opinions anyway.

Good luck and let us know what you decide.
Paul