A .30-06 is a good all around choice, but for what you will be hunting...there may be better options. You might want to look at a .260, .270, or 7mm-8...these probably offer a little more versatility in lower bullet weights. All would perform excellent on deer. A far as recoil goes, yes you are big enough to handle any of those...but it' s more mind over matter. You need to make sure you can handle them mentally. It doesn' t matter how big you are, if you are the least bit recoil shy...you will suffer big time in accuracy. Try and find someone with a gun of these cal, and shoot it and see how you do. The .260 and 7mm-08 have fairly low recoil.
As far as guns....stay away from the rem 710. It' s junk. The rem 700 adl is a nice gun, and reasonably priced...(around $350) but not really in your price range. Savage makes nice reasonable guns as well, but still not in the price range youre talking about. If you are dead set on spending $200 or less, your options are limited. You can look at H&R/NEF single shot rifles...they are nice and won' t break the bank. Pawn shops are hit or miss. If you don' t know alot you can get burned. There are some good used guns out there, but also some real junk. If you know someone selling a gun, that may be an option too.

I think you may be better off waiting a while and saving up some and getting what you want(new). Also, don' t forget optics. You will need to spend some $ on a decent scope....I recommend not buying a cheap one. Good luck, hope this helps some.