I' ve shot and killed game with all three, and they are all perfect for your needs. Since the 7mm-08 and the .260 kick less, I' d go with one of those.

I am going to be real honest here, and I am going to say that you will never see a lick of difference between the killing power of either. The sectional density and penetrating ability of both 6.5mm and 7mm bullets is legendary, and in my experience both cartridges are lethal all out of proportion to what paper ballistics would indicate. And if held to it, I' d say the .260 Rem is every bit as deadly, if not more so, than the 7mm-08.

For deer, in the 7mm-08, I' d use 139-150gr bullets. I' ve had the best luck with the 139gr Hornady Spire Point Interlock, 140gr Nosler Partition and the 145gr Speer Grand Slam. With the .260 Rem, 120-129gr bullets should work best for deer, with my personal favorites being the 125gr Nosler Partition and the 129gr Hornady Spire Point Interlock.

On elk, try the 150 or 160gr Nosler Partition in the 7mm-08 and the 140gr Nosler Partition, the 140gr Speer Grand Slam or 140gr Trophy Bonded Bear Claw in the .260 Rem