I've got a Rem 700 and an A-bolt, neither in the rounds you mentioned. Both are excellent and both will suit you well. Go to your local gun shop and put both to your shoulder, close your eyes, make your decision based on which feels "right" to you.

I personally believe all three rounds you chose are more than capable of taking the deer and hogs you seek. The 7 mag will be better for longer shots but the '06 and .270 are more than capable of reaching animals to 300 yards+. The 7 mag is more expensive to shoot than the other two. Personally I would choose the '06 because it allows you to step up to bigger bullets in case you ever decide to seek larger game.

In any case, both rifles and all 3 cartridges are excellent, you can't go wrong.