What distance will you be hunting? If you are hunting like we do, almost anything will work. We seldom take a shot more than 75 yard and more like 10-40 yards is normal in Georgia woods. I would suggest buying something that you can get ammo for a reasonable price. Just to toss out another suggestion, I have killed a lot of deer with 7.62x39. Think SKS, AR 7.62x39, AK, and a lot of other rifles shooting $5 a box ammo. Mine was AR based and the deer in my avatar is not the biggest I have killed with it.
^ This. What type of area and what distance are you hunting. If you're hunting open areas, and you want cheap, get one of the single shots (CVA or H&R). They generally run under $300, they are lightweight, and they make good suppressed guns. If you are hunting brush, get the 30-30.
I'd go real cheap out of the gate, and if you decide hunting is your thing, then you can pick up something nicer later on and use the cheap gun as your rain gun. I hunt with an AK, AR, or a single shot CVA when it's raining. I have under $300 in the CVA, and that includes threading the barrel to shoot suppressed.