.270 or .308 for Beginner Rifleman

[mtbkr]

Hi all,
I'm just getting into shooting and deer/elk hunting and looking to buy my first hunting rifle. Will certainly be picking up a .22 for practicing lots at the range.

I'm looking to buy both the .22 and the hunting rifle now so I can spend the next few months practicing my shot before hunting season.
I was set on a Savage 111 Trophy Hunter Package in .270 win (moderate recoil, just hard-hitting enough for elk, flat shooting...). However, someone was trying to convince me to pick up a .308 so I could buy cheap surplus ammo so as to be able to practice a lot with the big rifle.

My question: Buy the .22 and the .270 - practice tons with .22 and some with .270 OR...
...Buy .22 and .308 and practice lots with each.

Thanks all for the advice!!

Cheers