Are you looking to go new or would you be open to used? There are a ton of good deals on used firearms, typically with the scope already mounted. Being hunting rifles, many of them were only shot enough to sight them in.
As far as brand, that is as much a personal choice as anything. For newer rifles, I've really enjoyed shooting the Savage rifles with the AccuTrigger.
For caliber, I personally shoot 7mm mag, but I think something like a .270 would meet your requirements pretty well. It shoots flat, is widely available, and can easily take both elk and deer.
Rockin a 327 SBC