The30/06 is indeed a great deer rifle.
The difference in rimfire and centerfire is thus: rimfires are normally small caliber rifles that have the priming compound in the edge of the case rim at the head. The .22 LR, .17 HRM, etc. are the best known examples. They carry a much smaller powder charge due to the small case size, and are not generally intended for big game such as deer, etc. Most states outlaw them for big game hunting.
Centerfires are casings that use a separate primer in the center of the case head to ignite the powder charge. They are generally much more powerful rounds than rimfires, and usually can be reloaded, as where rimfires cannot due to the difference in ignition types. i.e....the centerfire primer can be removed after being fired, and thru the reloading procedure, a new primer, powder and bullet is placed in the casing to be fired again.
I hope this is what you are looking for, and that I haven't bored you with this very basic explaination if you knew this already......