Since your budget is $750 and you are thinking of a BLR in 308, it would not be a bad choice and you should be able to find one within your budget.
The same rifle in 243 or 257 Roberts (if you can find one) would also be decent choices for deer, or deer and black bear with the 257, or deer to elk with the 308.
As mentioned, there is also the Savage Model 99's and the Winchester Model 88 in 243, 308 and 284 Win, of which the 308 would most likely fit within your budget.
A Marlin in 35 Rem would also work well for deer and black bear and should be able to find within your budget.
The Henry Long Ranger is also available in the 6.5 Creedmoor now, just not sure of their pricing.