It's tough to accomplish all your goals adequately in one purchase, but that's okay cause you can buy one now and get another later. If you're wanting to shoot out to 200 or so I would say go with the .17 HMR. You can pick up a Savage fairly inexpensively. As it relates to deer, .44 mag in a lever action might be a good choice as others have suggested. I don't subscribe to the one gun rule though. You need more than one club to play golf and guns are the same way.
I'd recommend the Ruger 77/44. Bolt action 44 mag. Very slick gun