IMO any caliber will kill a deer with an accurate well placed shot... I would suggest a caliber that you can also use for other hunting adventures like woodchucks or coyotes so a caliber like the .243 would be great... or even the .223... granted that is a tad small but its travelling fast so that makes up for the loss of bullet weight... I agree with going to your local pawn shops or even gun shows in your area to find a decent deal on a used gun. If you have a sporting goods store like I do in my area you can always do a lay a way... Thats what I did with my AR-15... Check your local paper as well... Someone somewhere may need a few hundred dollars and is willing to foolishly sell their firearm to come up with the money!
Good luck in your decision and Good luck in the field!