The 7mm-08 is a very versitile cartridge. You can't go wrong with the .308 family of cartridges (.243, 7mm-08, .308, .338 Fed and .358). Here's a portion of a G&A article...
"The 7mm-08 Remington was derived from a necked down .308 Winchester case (7.62x51mm) and was touted as a new 7mm cartridge designed for short-action bolt rifles that equaled or bettered cartridges in its class.
During the load's development, Remington found that necking down the .308 to 7mm resulted in a cartridge that was inherently accurate, like its parent .308, and over normal ranges the trajectory was slightly better. It is ironic that the wildcatters and silhouette shooters had discovered the same cartridge 20 years before. Like other wildcats from the past, it sometimes takes a while for manufacturers to realize the potential of a new chambering.
With the velocities developed by the 7mm-08 using a similar weight bullet to available .30-caliber projectiles, the higher ballistic coefficient of the 7mm had the advantage of developing more energy and a flatter trajectory as the range increased. Along with the moderate recoil, great selection of bullets available and downrange performance, it's no wonder that silhouette shooters adopted the 7mm-08 so quickly.
For hunters the 7mm-08 is a great medium-range cartridge that is capable--with the correct bullet--of taking big game up to elk with no problem. It is a great cartridge for women, young shooters or anyone who is sensitive to recoil. Even in the lighter rifles the recoil is very tolerable."