Best rifle for target shooting, plinking, and varmint hunting?

When I first read your thread title I though 223 all the way, BUT a 223 is not a great deer gun(which is something you would like to do) A 223 is definitely not a good deer gun for a new hunter and may be illegal for use on deer in your state. The benefits of the 223 are it will give you the added power and range you want over the 22 but still have cheap ammo(not as cheap as the 22 but less than almost all centerfire calibers $5 a box of 20) A larger caliber like the 243 will do everything the 223 will but also take deer the problem is there is no cheap 243 ammo(12 to 15 a box of 20). If you bump up to a 308 you can hunt anything in the lower 48 and still find ammo pretty cheap for plinking($8 a box of 20). The problem with the 308 is even though its recoil is pretty mild for a high powered cartridge it still would be a lot for someone who hasn't used anything over a 22 and its going to be really loud. Personally If I was you I would get a 223 and learn to shoot it well then when you are ready to deer hunt get a high powered rifle. The 223 is a great cartridge to make the step up from 22 to centerfire rifles. You should be a able to find a good 223 bolt that will fit your budget.