+1 what most folks have said. The 7mm-08 is an excellent choice. Basically ".270 or-- if you prefer--.280 Lite" and that's no denegration. The .270 will send the bullet down range a bit more, so if seriously contemplating frequent shots past 300--"long range shooting," I'd go with that. Otherwise, the 7mm will do what it does--in a shorter action, which also equates to slighly shorter OAL in otherwise apples-to-apples rifles often firing from the same 22" barrels (some .270s are 24" as well)--and offered in some specialized smaller formats than .270 (see Rem Model 7 and a Ruger equivalent IIRC) as well. To me, the 7mm-08 is the ultimate "Mountain Rifle" in just about any of its platforms. We're not talking much here, but every oz counts when you're doing a lot of trekking. Since you say you stand mostly, where longer OAL isn't really a factor, and may get into the longer range stuff, hard to go wrong with the .270. Otherwise, pretty much a toss up...and I'm a big (huge) .270 fan and 40 year shooter. A 7mm-08 Featherweight will be my next bolt rifle purchase "just because."
Now, if you want to be a bit different and get into semi-exotica, get a .35 Whelen. (Recent thread on that somewhere here I think). Great round, non-magnum, regular (.270, 30-06 etc) action whopper--think .06 Plus) that excels on elk-sized game...but although certainly effective on deer as you might think, also largely unnecessary.