You are at the right Club for suggestions...
First off your idea of cartridge choices are great.
For what you are looking at 7mm-08, 308 Win, 270 Win, 30-06 will all work great. Basically there is not alot of difference on Deer for any of these choices. All makers chamber rifles in these because they are the most popular.
To keep under you limit of 500.xx and it be new not a used rifle you are going to be at the entry level models. You should plan on spending about 150.xx of your 500.xx on a quality scope. You will not miss a shot at a fantastic Deer because of your entry level rifle, but a crappy/cheap scope could cost you an animal. Some entry level rifle packages include a scope with the rifle for a slight increase in price. These package scopes are junk.
I really like the Marlin XS7/XL7 rifles. They are an entry level that doesn't feel or shoot like one. I like the Marlin because they have a good trigger, barrel, and the action is nice and tight. Ruger is bringing out a new entry level rifle that is worth asking to see. Ruger makes the really nice M77 Hawkeye bolt action, and this new one is an offering at the entry level pricepoint.
Take a trip to a large store with a big selection and ask to see their bolt actions at the 350.xx pricepoint. You will be supprised at the large selection they will have. Ask their opinions, but go with what fits you best.