If you plan to use it all for defense (either home defense or carrying), then I'd suggest a .357 magnum or a 38 special. You could use 38 wad cutters for the small game hunting, or even some standard 38 loads.

For strictly small game, ruger makes some dandy .22s. At less cost, there are heritage revolvers.

If you can afford one, A "do it all" gun would be the Ruger sp101 in 357 magnum, 3" barrel. It makes for a light trail gun and it works well for concealed carry if you have a good belt. I use a belly band appendix carry and it works fine. (It's a little big for pocket carry). If you aren't concealing it, they make a 4.2 inch barrel that has fiber optic sights. It can be had in in .22lr as well.