I have read that the 3-9x or the 3.5-10x is considered the standard variable power range for scopes for general purpose hunting. Imagine, a .30-06 may be used for hunting varmints, deer in heavy timber, mule deer on open ranges, pronghorn antelope, elk, and moose. The .30-06 may not be optimal for all these circumstances, but it can be used successfully in all these circumstances. What variable power scope range fits this range of hunting situations best? As I said, it seems a lot of people feel the 3-9x or 3.5-10x variable power range fits this very well. The .270 has a lot of the same broad capability as the .30-06, but concensus begins to soften on whether the .270 is adequate for elk and moose. Still, you get my point. On this basis, the 3-9x or the 3.5-10x range seems suitable.

On the other hand, you say most of your hunting will be in heavy timber, and if tuning your hunting gear to this situation is important to you, going with the lower power range 2-7x probably makes more sense. Remember, even at 7x you have a lot of magnification. When hunters used a fixed power scope, they generally chose a 4x for general purpose hunting. If they were choosing a long range, open country scope, I think they may have gone with a 6x scope, but this was considered kind of a specialized rig. 7x is likely only to be limiting, if that, on shooting pronghorn antelope at long range. If you choose to use your .270 on elk and moose at long range, the fact that these are such large bodied animals means that 7x probably is not going to limit you (7x for an elk/moose at 400 yards is probably a bigger sight picture than a whitetail at 400 yards at 10x, just my guess).