First, welcome to the board dodger02!
Savage is a hard gun to beat for the money! I would not hesitate to buy one! You mentioned the Browning A-bolt, it is a good gun too, along with the Winchester and Remmington.
You also mentioned a 500 dollar range limit. You won't be able to buy a new A-bolt and put good glass on top for that price!
For that matter, you'd be hard pressed to get a Savage and a good scope for 500 or less! You could probably get a new Savage package deal, with a cheap scope for less than 500, but I would invest in a good scope like a Leupold or Nikon as soon as I could afford it.
Also, you said you want a .270, that will be as good of a deer caliber as you can get! The other calibers you listed from .243 on up would be good too! I wouldn't recommend any of the .22 centerfire calibers for deer hunting though!
Remember, what ever gun you get, will only be as good as the glass on top of it is, so don't skimp on the scope! Good luck!