Shooting 22's is a great suggestion.. However, In my experience it can be much more frustrating than most make it seem. Once you are comfortable enough to shoot better than 1moa, is when it starts getting frustrating.
My 22 rifle with regular ammo (not the cheapest bulk but not the expensive stuff) cannot produce better than 1moa. Maybe even no better than 1.5moa. When I'm used to 1/2moa out of all my centerfire rifles, 1moa just doesnt cut it. You never know if its you doing something wrong or you got a bad round. This can lead to bad habits being formed, as your trying to fix something in your form that might not need fixing.
Now, I know that if you buy a high quality 22lr and shoot expensive 22lr from it, then you can get pretty good results. However that defeats most of the reasons of practicing with a 22 in the first place! If you can afford to buy a $700+ rifle and practice with 25 cent rounds, then you might as well get a 223 bolt rifle and shoot your reloads (both of which will cost less!). The only reason I can see the 22 having an advantage is if you absolutely have nothing longer than 200 yards, then it can help you tune your wind reading.
Who knows, maybe its just my 22 that isn't a 1/2moa rifle. I've heard the relatively inexpensive bolt savage's are fairly accurate. My marlin 795, not so much.