You should use 180 class bullets or bigger with the 300 RUM. Why? Because you have a ton of powder, take advantage of it and produce some energy. Also because after several hundred yards, even though the MV is slightly slower it will still yeild a flatter trajectory to 1,000 yards due to a higher BC with SOME 180+ bullets. Also at 300 RUM velocities anything less might not hold up good enough to deliver damage far enough into a big critter. You need more mass to get the bullet to the vitals. These are just a FEW reasons.
Also I have had great luck with the 178 AMAX, 180 AB and the 200 AB. I use the 178 for deer, sheep and black bears. The 180's and 200's for everything bigger. It depends on my mood.