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I agree with the Savage Arms recommendation for a rifle.
You can buy a Savage Axis XP for about $375. That's brand new too, with a scope. Sure it's not a high end gun , but you'll kill a lot of deer with it if you learn to shoot. I own several Savages, they all are very accurate. I love them.
For caliber? .223 is the smallest you'd ever go. In my state it's illegal to hunt anything with an AR-15, or any semi auto gun for that matter. I think the perfect whitetail deer caliber is 25-06, or 7mm-08. Both are very similar ballistically, only the 25-06 you can get lighter loads for smaller game, and the 7mm-08 you can get hea ier loads for larger game.
Nothing wrong with a good old .308 either as others have suggested. You can get ammo cheap, so it's more economical to shoot. If you get a more exotic caliber, it may shoot awesome, but ammo can be hard to find and expensive. For a beginner, you'd never reap the benefits of a more exotic caliber.
If you're actually that poor, why not start off small? Get a bolt action .22, and small game hunt. Y9u can get a used .22 for well under $200. Put in a scope and go hunt during small game season. Honestly squirrel hunting is about my favorite to hunt. You can also hunt woodchucks, crow, pheasants, grouse, rabbits, and other small game with a good .22 caliber gun. You could spend more and get a .17 hmr, and hunt all those same animals, but also hunt some larger animals like turkey with a good .17 hmr, although I like a bigger caliber for turkey, they do work.
If you spend a little more you could also get a shotgun which opens up possible options to hunt as well. A 20 gauge shotgun will kill all those small animals I listed before, although you need to be closer than with a rifle.
