Definitions and advice

Question
I would like to know what the difference is between a rimfire and centrefire weapon? Is one better than the other? Also, I'm looking to buy a lever action rifle, possibly a .22. Any thoughts as to brand, ammunition, etc.? It will be mostly used for target shooting and  small game. Eventually I would like to move up to a rifle large enough, also lever action, to hunt larger game.

Answer
A centerfire cartridge is a cartridge in which the primer is located in the center of the cartridge case head. All high power rifles are centerfire. Rimfire cartridges (.22, .17 cal.) are low powered cartridges where the primer is the entire base of the cartridge. The .22 is extremely popular and cost efficient. The range is not great and unless you are varmint hunting at 50 yards or less...move up to the .17 HMR
I would recommend either a Henry,Browning or Winchester. Better yet, the DEFACTO standard in quality entry level .22 rifles is the Ruger 10/22 semi-automatic rifle. Very good overall and can be customized to almost no end. AS far as moving up to a serious centerfire lever-action rifle...Marlin and Winchester are the more popular. There is not a lot of ammo choices out for the .22 compared to a full size lever action 30-30.