I agree with the previous post concerning a 22 rimfire as a first rifle. You can shoot matches later, learn the fundimentals now, all with the same rifle. A good 22 rimfire is the most versatile rifle you can have. And the most fun IMHO. Good for plinking, pests, matches, and cheap ammo too.
I always recommend starting with a bolt rifle. Since you are learning the basics, now is the time to learn to run a bolt gun.
The little CZ 452 American is generally available for less than $400. Start with the open sights. Learn to use them. Then, replace the open blade with an aperture from
http://cz452.com/ Learn to use it. Then mount a good quality optic. Learn to use it. Then move to a centerfire rifle.
I'd prefer 308 as it's more versatile. But, if you only intend to shoot paper, the 223 is probably a better choice. You have a myriad of choices in bolt rifles - again, CZ makes a dandy - and of course there's the AR15 platform. The sky is the limit there.
BTW, my .22 LR rimfire CZ 452 American easily shoots sub .25 groups at 25 yards. Bear in mind that I am not a precision shooting kind of guy, more of a field shot here. A good benchrest guy with match ammo could reduce this easily.
If you go with the CZ, I also recommend Brookie's trigger kit.
http://cz452.com/ The best $9.00 I've ever spent. It took mine from ~4.5# and a lot of creep to ~2.5 and no creep. It comes with springs to bring it down even more, but I use mine in the field and ~2.5# is about as low as I want to go. If you are using it strictly off the bench, you can safely half that with ease.
I'd also recommend Jeff Cooper's "Art of the Rifle." It's not geared toward target shooting, but rather gives a great overview of field use and why the rifle is "the Queen of the battlefield." The drills outlined in the text are essentially an abbreviated syllabus from the 270 General Rifle class. You could easly modify the ranges on these and shoot them with your 22. This would provide a good adjunct to your bench practice.
Good luck, and welcome.