While I love my 7mm, for a first Rifle for hunting what you listed, there just is no beating a 30/06. It does everything you need and ammo is cheap.

If you want to be a little different for whatever reason, the 7mm Rem. Mag or 270 Win are nearly the same in all ways. I went with 7mm since one of my main hunting partners shoots the same so I figured I'd get the same caliber as him for all the normal reasons (sharing shells if one runs out, same balistics, same performance).

I do have a 30/06 my Dad just handed down to me. Crappy scope and doesn't shoot as well as my Tikka but I should try to hunt with it some. My wife uses a 270, and while a great round, she's only had medium luck with it (somewhat due to bad shot placements, she has a new Bushnell Elite 3200 that Santa just got her, hopefully that'll help some). Still, for most guys that can handle a heavier gun and more recoil, I think they are better served with bigger than the 270.