I did my first hunt last year as well. Seen a Momma with a yearling the first time (beautiful site and so-o-o quiet), and the second time was a large boar.
I had a 7mm.... but I think it was a little overkill. I didn't bag him as I shot him low in the brisket and he got away... my first animal I lost and I am upset about it to this day. Enough of my story though....
I guess your choice b/w the 270 and 303 would be how comfortable are you with scope/iron sites. I would choose the 303 myself.
As per ideas... my brother in law passed this to me. Bears are like Dogs.... get a barrel and bait a few weeks before season. Bang the barrel a few times when you get there in the AM like a dinner bell, and take the barrel away at night. This will have them smell that food was there and they should have came when called. by the time hunting season starts, you shouldn't have to bait.... just bang the barrel.
Also, in the area of the bait, pour old deep fryer oil on the ground. When a bear comes, they step in it, leave to go home, track the smell of fries, onion rings, etc through the bush, which will lead the other bears right to you.
They smell really good, poor sight, and pretty good hearing. Stay still *because although they don't see well... they will see movement, stay quiet, and don't go to the club the night before. lol. Bears are really shy.
Hope I was of some help.