If you like the Rem 700 in .243 you can rechamber/barrel that for .308.
If the rifle is only for elk, then get a Stevens Model 200.
Here's one in 7mm-08. http://www.gunbroker.com/Auction/Vie...Item=306340519
The 200 is easily accurate to moment of elk. 350yds is within the range of most standard cartridges. You will have to figure bullet drop into that, but not much.