The 7mm-08 has been taking elk since it became a commercial cartridge.
I would use premium bullets, factory loaded, like Hornady or Federal Premium, since FP use Nosler, and Sierra bullets.
The lightest bullet I would use would be a Nosler 140gr Partition, or the Accubond. The Accubond will shoot faster and flatter, and hit with more energy than the partition.
But, Nosler has a 150 gr Accubond, and I think this would be a better fit, since it's heavier, bonded, and retains it's energy better than the 140 gr.
If handloading, I would use one of the new powders, like RL-26, or Winchester StaBall 6.5 to eek out the most velocity possible without spiking pressures.