I'd recommend you give your terrain some consideration when selecting magnification. If you're hunting in the woods, the low side becomes more important. If you're hunting on the prairie, the high side takes the lead.
As an example, most of my deer hunting is in the woods. I generally can't see much but trees beyond 200 yards anyway. However, I'll often jump a deer and need to pick it up quickly in the scope, so a 3-9x serves me quite well. Conversely, my pronghorn hunting is always out on the prairie. The limitation there isn't so much how far I can see but at what point the bullet I launch no longer has the ability to take an animal down cleanly. Accordingly, my pronghorn rifle is topped by a 6.5-20x.
I have a short-barrelled 700 LTR in an AI chassis in .308. 600 yards is nothing for that rifle - on targets. It's heavy though, and isn't my preference for hunting. A Manners is going to be far, far lighter than my AI, but with a heavy barrel already, adding big glass to your rifle is going to drive the weight up. Something else you might consider. When I carry my AI, it's usually in a pack (a GS2). That doesn't work for hunting, at least for me.
I own quite a few Burris scopes and I've been happy with them. I suggest you hunt for a couple of seasons with what you already have and see what you find yourself wishing for in terms of magnification - more ... or less of it. 3-9x covers a lot of situations very well, however.