The 7-08 is an excellent choice as an all around caliber for varmints to elk. I also use it with outstanding results when hunting coyotes out in the desert. 120gr bullets for varmints. 120gr Barnes TSX for deer. 154gr Hornady IB for Elk.
Mine is a Rem 700, SA, 7-08 Classic. This rifle has been completely accuracy tuned, free floated barrel, HD recoil lug, pillar and glass bedded, chamber re-cut to match specs, muzzle recrowned with recessed 11 degree crown, Jewel HVR trigger set to 2 lbs, NF NSX 3.5 - 15 x 50mm, NP-R1 recticle, 20 degree one piece NF base and rings.
Groups consistently at 1/2 inch 100 yard for initial sight in. Once accuracy is confirmed for bullet weight , powder type and charge. Zero is reset for 200 yds.
Come ups are develop for 700 yds varmints and deer. 300 yard zero for elk. come ups to 800 yds.
Gonzo