I had a 10/22 many years ago and sold it. I got into centerfire rifles for deer hunting.
Maybe 4 years ago, I got a Browning SA22 and I'm kicking myself for not having done so earlier. Light, accurate, and a lot of fun to shoot. Not too bad for grouse in Washington State, either. (Yes, we're allowed to shoot grouse with a rifle.)
That was the basis of my suggestion to get a "good" .22 that you would enjoy later, after using it to develop the fundamentals of shooting.
Also, there's a world of difference in .30-06 recoil, depending on the rifle. (As others have said already.) I have a cut-down Winchester 1895 lever-action in .30-06 that is a little bit of a challenge to shoot, due to the drop of the stock and its relatively light weight at 7.5 lbs. On the other hand, I have a heavy-barrel Winchester M70 clone in .30-06 that weighs 13 lbs (w/ scope), and the recoil from that rifle doesn't even bother me. Same ammo in each rifle. My Garand has a recoil that seems to be in between those extremes, which makes sense as it weighs around 9.5 lbs. And a Ruger No. 1 that weighs the same (9.5 lbs) is much easier to shoot, as it has a Limbsaver recoil pad instead of a steel plate!
Summary: The "typical" .30-06 hunting rifle is going to weigh around 8 - 8.5 lbs. Set up with a good recoil pad like a Limbsaver or a Decelerator, it isn't that difficult to learn to shoot. It will be more difficult than a .22, and the possibility of developing a permanent "flinch" is a real one.
Re: AR15 in .223 as a substitute for .22LR, I suppose that would work. Recoil is very low, though not as low as the .22LR. The "old school" way of learning marksmanship is to learn sight picture, trigger, and breath control in different positions, without having to fight the distraction of recoil. I think the Army just drops recruits into the M16/M4 whatever it is designated, without training first on a .22LR "trainer" version of the same rifle.
Long ago, I believe the Army had some kind of .22LR trainers for riflery, but by the time I got exposed to the Garand in the Navy, there was no introduction. You got the centerfire round to practice with, and had to shoot for score a couple of days later!
Good luck.