If long range is your ultimate goal, then look beyond your needs for today. The 308 is no slouch, but it gives up a lot in terms of performance at longer distances. For now, 600 yds sounds like a long way off, but you may just be surprised at how quickly that becomes a "chip shot" on large game.
I'm a longtime Rem fan, but recent purchases (incl. new SPS and Sendero models) have left me very dissatisfied. I am now a recent convert to the Savage line. If it were me, I would go with a 7 Mag, 6.5x284, 260 Rem or maybe even a 300 WSM
Final piece of advice: Don't settle. Stay within your budget, but get exactly what you want. If you can't find the right combo in 308 - then wait. A used stick in 308 with your specs will come up for sale soon enough. Shooting is very much a mind game and you don't need any "what if" or "I wish I had" thoughts nagging at you every time you squeeze the trigger.