Chevy...I have a couple of thoughts...1) What type big game will you be hunting??? 2) What distance do you expect to be shooting???

If it is primarily deer within 300 yards...308
But....You could also add 25-06 (which I don't care for simply because of the length of barrel and around here lack of diversity of factory loadings)
Two other excellent choices would be 7mm-08 and .270....The 7mm-08 has gotten very popular around here because it kicks less than a .270/30-06....
And kills deer just as dead.

If you will be hunting game larger and tougher than deer...30-06 would be hard to beat.