If you are going the route of a .22, my suggestion is to start with a bolt action with iron peep sights. It is too easy to get into bad habits regarding trigger control with a semi-auto. Trigger control and breathing is key in shooting a rifle with precision and consistency. Iron peep sights build better discipline in sight picture. You can always add a scope to the rifle after you master the peeps. That's how I learned to shoot as a kid. 17 HMR is also a great round to start with, but .22 is still cheap enough that you can get lots of trigger time and you wont break the bank. A lot of high-speed carbine courses allow and even encourage the use of .22 to keep the costs down. Try going through a carbine course over a week with 2-300 rds of .223 a day. Cha-ching.
Back to the .22. Practice at home working the bolt and dry firing (you can use a couple of snap caps if you are afraid of wearing the firing pin down.) If you practice manipulating the bolt enough, you can get to the point where you can keep your eye on the target as you cycle through.
Finally, if you get serious enough, go take a precision rifle course somewhere. I would suggest TJ Pilling at Tiger Valley, Bill Davidson at Tac Pro (In Mingus, not too far from Abilene) or Jacob down at Rifles Only near Corpus.
My .02 cents
NRA Certified LE Patrol Rifle Instructor
Texas State Guard
3BN, Maritime Regiment