Any straight shooting 22LR (LR stands for Long Rifle)in good condition, even a used one, will serve you well.
Since you are new to hunting, I would visit a few local gun shops looking for a good used 22 LR that you can afford. Ask questions of the shop owner, most are very upstanding knowledgable people and will give you good sound advise.

I would avoid all 22 centerfires at this point in your learning curve, they are over kill on squirrels and rabbits.

22 LR Ammo is cheap, so you can shoot a lot. Have fun