270win, 30-06 etc... don't kick IMO in a standard weight rifle.
300win.mag. type cases/cartridges kick!
ie the 270 is very comfy to shoot, fun, nice, easy, 300mag, 340wby mag etc... are not fun too shoot, they're manageable etc... but I would never choose a 300mag to go plinking at the range.
You're options are grand from .270win, to 300mag, and since you mentioned moose, 338win.mag is a pretty sweet round, great for deer to moose!
I like the WSM's, the 2 most popular are 270 and 300wsm and are here to stay IMO, the 7mm and 325wsm not so sure about... although the 7mm is a sweet round but best doesn't always win the race.
I'd strongly consider the 7mm Rem.Mag, .300 WSM, and .338 Win.Mag.