I recommend a good .22 rifle....I like the Henry AR-7....About $250.00 new. Mine is accurate up to over 100 yrds, extremely reliable.....this is for small game. The Ruger 10/22 is nice, but costs over $100 more.
For home defense especially if you are a gun-beginner I would recommend a .357 revolver....nothing fancy or slide/safety, to manipulate, etc. just point and boom...and you can use .38 S&W's, .38 special, +P+, and .357 magnum ammo.
or a 12 ga shotgun personally I like a Remington 870...very reliable many accessories and inexpensive...about $300 anywhere (used).