.270 if you don't want to worry about range (can be set up to +/- 3" out to almost 300 yards, which means you just put the crosshairs on the target and shoot, out to that distance.)
.308 only if you want a compact rifle, and then consider 7mm-08 Rem, which is sort of the "short action .270 Win". Otherwise get a .30-06, which is the same cartridge in a longer case, with more versatility and better velocity in factory loadings. No reason to get a short action then put a 24" barrel on it.
.300 WSM if you plan to hunt in the mountains, backpack in, and hunt for elk, and therefore want a compact rifle with extra oomph. Same applies: no reason to get a short action and put a 24" barrel on it.
Out to 300 yards, the performance of a .300 WSM and a .30-06 with standard factory loadings will be indistinguishable on deer, both in terms of trajectory or energy. A chronograph can tell the difference, but a hunter can't, except that his shoulder will hurt more with a magnum round.
Past 300 yards, you'll want to choose very carefully. A light, compact rifle may be a poor choice for very-long-range accuracy, regardless, though it's more pleasant to lug around.
A .300 WSM is more expensive, slams you harder, and burns up barrels faster. There's a reason that .30-06 is still the most popular hunting round in North America, and .270 is (I believe) the most popular deer-specific variant. It's a necked-down .30-06, in case you didn't realize that.