Shooting prone, unsupported can be rough. Appleseed will teach you how to use a sling. You'll be amazed at how much steadier it is.
Proper position, trigger squeeze, breath control, these things all go into becoming a good shooter.
I love the Ruger 10/22 for lots of reasons but if you ever get a chance to shoot a real target rifle like an Anschutz, Winchester 52 or Remington 40x, with their marvelous triggers and some good iron sights don't pass it up.
Some of the experts on the forum here regularly recommend the Civilian Marksmanship Program (CMP) Instructional manuals. Here's a link to their page.