I'd stay away from the magnums, until you need one. A quality made rifle with great glass (scope) will serve you well. Based on your initial post, you wouldn't be wrong choosing .270 or 30-06, with a slight lean to the .270. (or split the diff and go with a .280Rem*)
For a price range, you're looking at $1,000-$1,300 for a decent/serviceable rifle and a pretty good scope. Any package for less will get you the same rifle and a scope of lesser quality.
*ammo may be harder to find than the other 2 calibers.