Think also about a .30-06.
While most people these days prefer a scoped rifle, you can still hunt old school using a rifle with iron sights. Thus, you can get by initially with a rifle that does not have a scope. You should look around for special deals on rifles such as at a grand opening of a Bass Pro Shop or a Cabela's. Several years ago I bought a Remington 700 ADL synthetic stocked .30-06 for $280 at a Bass Pro Shop grand opening. You could check pawn shops, but know what things are worth before you do. I have seen many over priced guns in pawn shops. Ask people you know if they have an old hunting rifle they will sell to you.