With a budget that high, I would look to get an heirloom quality hunting rifle. I quit buying "budget guns" several years ago and have since replaced all my budget guns with quality rifles. Sure, budget guns shoot fine and will get the job done, but I have the money for better fit and finish these days.
Anyway, If I were looking for a .308 with $1200 to spend I would get either a Winchester Model 70 Supergrade (beautiful stock and the best production action ever), or a Winchester Model 70 Extreme Weather.
The Supergrade has a beautiful maple stock, high gloss finish, AND a beautiful bluing high gloss finish on the barrel and action. This is a truly beautiful gun, but will require some maintenance to retain its beauty if you use it.
The Model 70 Extreme Weather is a bit less expensive, it has a more durable finish on the stock, and it is stainless steel on the barrel and receiver. This model is more intended for hard use but still retains all the features of the Supergrade.
If those two rifles are a bit too high on you budget (they are both right around $1200), Then you can look at the Model 70 Fetherweight or Model 70 Sporter. The Featherweight and sporter I think both have the controlled pre-1964 action which is what you want in a model 70. Both of them can be found for $800-$900 each.
I do not work for winchester, my latest hunting rifles are custom builds and I have some $$ into them, but if I were to buy a production hunting rifle....Any of the above is what I would buy, and they will still be valuable many years from now.