You really should just get out and start looking around for something that catches your eye and then do some research on it. These days, all of the larger manufacturers have lesser expensive versions of their rifles and apparently, they all shoot well.
Since I'm in south Louisiana, we don't really need a rifle capable of precision long range accuracy, so almost anything that goes boom will do. If I were you, I'd just look for a model with a stock and trigger that I like.
For starters, I'd look at models from Remington, Savage and Tikka and concentrate on the ones in stainless, if possible. You may also do well to take a look at the Stevens models, if you can find one. I think they were discontinued.