Well, tell us a little more............You said "big game".......Does it include big bears, elk, moose, or deer-sized critters only? There are so many choices available that we need specifics. I hope you realize that almost everyone on here will be more than happy to dish out their personal likes/dislikes and wish lists..
Personally, if I was hunting big bear, I would carry a 338 as minimum. Great elk and moose medicine too, and i have to admit I've even killed a couple of whitetails with it when my go-to deer gun wasn't available.
The 7-08 is gaining quite a following as an efficient deer rifle, but many others will fill that bill also. The old 30-06 is a proven workhorse for almost all NA big game hunting, with maybe the exception of the largest bears.
As far as a scope goes, I'm pretty much a hard-core Leupold fan. Nearly all my hunting guns wear Leupys, with a few Redfields and a Weaver or two.
Whatever you choose, do the best you can to go first class with your equipment. It will be money well-spent in the long run.