Welcome to the DHC buddy. I'd recommend 243, 270, 30-06 but there will be plenty more listed as well from others.
Karl's recommendation is right on the $$, in my opinion. Find one in .308 or .270 and you'll have a great starter outfit, that also might fill your needs for many, many, many years!Welcome to the sport, it is more fun then golf and you can still lie about how good you are at it. Head over to your local gunstore with a big selection and ask to look at a Marlin xl7 bolt action rifle. This rifle offers a lot for the money and it has all the main features you will need. A good barrel, tight action, and clean trigger is all you need. This rifle will have them. Ask to compare this Marlin to others in the same price point and you will find what feels best for you. Don't be in a hurry to buy that first day, this is part of the fun. I always recommend a new shooter to plan on spending around $300 for the rifle, and another $200 for the scope. Whatever rifle you will end up with will last more than your lifetime. They don't wear out, shooters just decide they need an upgrade or change of pace.
Karl
Good advice.Hello and welcome to the site and to hunting as well. For your needs, I'd spend my money on a good condition used rifle already set up with a scope. As stated above Marlin lever actions in 30-30, 35 rem, 32 special, with a nice scope would serve your needs well. Don't over look good used Savage model 99 in 300 sav, 308. It's pretty hard to wear out a barrel these days so I would just make sure it's clean and shiney all the way down. I would think something between $275.00 and $375.00 would be available at most gun shows.