John: If you are planning to hunt tight woods, a lever action .30-30 with open iron sights would be suitable. If not, a bolt action. I would look for special deals for a rifle scope combination from a local sporting goods store, from Cabelas, or from Bass Pro Shops. Your budget of $500 is a bit tight, but this doesn't mean you can't find a rifle that will do good hunting service. Alternatively, if you could find a rifle for less than $300, I would look for a telescopic sight in the price range of about $200 from one of Leupold or Burris with variable magnification no higher than 10x on the high end (for example, 3.5-10x). Most hunting rifles -- no matter how cheap -- will do their job reliably and consistently. The same, regrettably, cannot be said of different telescopic sights. If you get too cheap of a telescopic sight, odds are it will be not very durable (shooting a deer rifle with a scope attached to it is like hitting the scope with a hammer hard everytime you shoot -- that scope BETTER be rugged).

As far as chamberings for a bolt action, I would stick to the traditional cartridges -- .30-06, .270, 7mm-08, .308, .7 mm Remington Magnum.