If you are going to be seriously hunting deer I would stick to a bolt action. chances are that you'll eventually want to hunt bigger game so stick with what's reliable, and most accurate.

The 7mm vs. the 06 question is one of personal prefrence. Either one will do very well. You are correct that the 06 does come in bigger grain bullets but the 7mm is extremely fast, which is where it gets it's knock down power, and the bullet itself may not be as big around but it will usually be longer and able to carry more kinetic energy than some other "bigger" bullets.

However, It sounds like you should go with the 06 because of it's affordability, durability and the wide range of ammo available.

There will be a ton of replies to your question, there always are when someone asks an opinion on this forum, everything from "you should get an SKS" to "you need a .270", or " a .300 is better...."
Don't listen to the hoopla....go with the 06.