I have a 7-08, in a Bergara ridge , that I bought last year, and have had a lot of fun with it. I settled on Varget, or cfe223. The Nosler 120bt, is gonna be hsrd to beat, they re designed that bullet, and a 708 will do it justice. Dont overlook a 120 TTSX, and a upper end load of varget. Nothing carries a ttsx home.
Also, tslk to Steve, at Hammer Bullets. He will set you up with the ultimate in hunting bullets, that wont break the bank. I have aldo done exceptionally well with RL16. Its a fun round to load for, ans will shoot about anything you set into it. Good luck, enjoy.