Josh
I agree with other guys who have said that you shouldn't discount what you have learned shooting your pellet rifles. A lot of us got started in that way and some of us still hunt with them. Also, and this is just my opinion, but you can learn a lot from hunting those squirrels and rabbits. Hunting a large whitetail buck is more like hunting bushy tails and cottontails than most people think. You learn how the animal behaves, what its food, water, and shelter sources are and what the optimum method of getting close enough to the animal to take your shot is.
As far as what gun and caliber and all of that junk. My suggestion is that you first get your firearms license so that you are legal and definately take both a firearms training course and a hunters education course. Then I would go to your local gun shop and get their advice. The reason for saying this is that they will be able to give you greater insight as to what calibers are popular (so you can get ammunition). They'll also be able to get you set with a rifle that will be better acclimated to your specific needs because they'll understand the what the hunting situation is most likely to be like. I personally have 6 or 8 rifles that I consider "deer rifles" because I hunt in two states and a variety of situations. I also use them for hunting other species of game.
Bottom line, alot of what you will see on here is just personal opinion. Everyone has their own style. Welcome to the forum and good luck
Indy