RE: First Rifle
Get the .30-06. While the .270 is not bad, the .30-06 will give you more flexibility. There will be arguments about this, but some people feel that the .270 is doubtful for use on Elk. I don't hear this same kind of doubt about using the .30-06 using 180 grain bullets on elk. You can use the .30-06 for predator hunting on up to elk and moose with confidence. The .30-06 is probably the most commonly available ammunition. If you leave your choosen loads at home on the coffee table when leaving for an out of state hunt, you can find .30-06 loads with appropriate weight bullets for the local game at any out of the way hardware store or grocery store. Granted, .270 ammunition is pretty common too, but the .30-06 is probably more common.
Over time you may accumulate other rifles that are especially well suited to particular game -- .25-06 for pronghorn antelope and deer; .338 Winchester Magnum for elk; etc. -- but the .30-06 can be taken on all hunts as a back up in case your first string rifle gets damaged or the scope knocked out of adjustment.
Again, not to disparage the .270, but I think the .30-06 wins for versatility.