Remember, you can easily "pimp" your 10/22... there are stocks, barrels, triggers, and anything else available for those rifles.
As for shooting issues, here are a couple of randomly selected thoughts:
1) Just my humble opinion, but I'd probably focus on the fundamentals of shooting first, then worry about ranging with the mil-dot system later. In other words, eliminate some variables. Instead of wondering if you missed because of a ranging error or shooting error, make sure that you missed because of a shooting error!
2) I also like the walk-before-run philosophy. Before you worry about nailing the 6" steel at 500+ yards, see if you can consistently print sub-inch groups at 100 yards. Then, once you know you're pulling the trigger correctly, you can start to deal with factors of wind, elevation adjustment, and atmospheric compensation, each of which will certainly affect your shooting at longer distances.
3) Take the time to dry fire from your shooting position on the range. First, dry firing is entirely free practice. More importantly, it might reveal some problems with your form that may go unnoticed under the recoil of live fire.
4) Look for the skilled people at your range. Find the guy/gal who is accomplishing the things you want to accomplish, and strike up a conversation. Most gunners are happy to share their knowledge with interested beginners, and you might pick up a few points along the way.
4a) If you can't find a skilled person at your range, attend a couple of rifle matches. Maybe spectate once or twice, try to pick up some tips, and then shoot the match with a purely recreational mindset (you don't have to win to have fun, or learn).
5) When practicing, remember that perfect practice leads more naturally to perfect performance. Have a purpose for the things you do, and think through each shot. What happened? What did you do right? What did you do wrong? What was the result? This may sound simple and elementary, but it seems to me that far too many shooters fail to analyze themselves, and settle instead for a healthy dose of mediocrity. That, of course, is fine if you are just out shooting to have fun. But, if you are trying to improve, there probably ought to be a few more considerations involved.
As an example of this idea, I've known more than a couple of mediocre riflemen/women who have probably fired more than twice the number of rounds that I have in my life, and still fail to perform at even a middle-of-the-road level. It is my belief that their lack of performance is not the result of some inherent deficiency in these individuals, but is instead caused by a lack of purposeful practice and training (even self training) on their part.
6) When you find a skilled rifle shooter among your friends, or among those shooters you meet at the range, you might consider letting them put a group or two through your rifle. In doing so you may discover that your rifle is capable of far more accuracy than you think, or you may discover that you're already doing a pretty good job of placing the bullet where it needs to go.