.22's are great "starters" and they are useful throughout your shooting career for working through problems or developing techniques. When you buy one of your own I recommend a Ruger 10-22 for it's accuracy and reasonable cost.
25 yards is a good starting point for learning with a .22 and you should keep it about there (my opinion) until you are well practiced and accomplished before attempting more distance. Prone groups of 4" are not really tight depending on the rifle and ammo you are currently using. With a good rifle, ammo and technique you should be getting close to "ragged hole" groups at that distance from that position.
I'm not sure what you perceive to be the difference between accuracy and precision. If you explained a bit it might help.
For precision shooting I like the "four-square" type sight in targets the best but it can depend on your sights...optic or iron...pick what works for you.
Look for a local NRA Rifle instructor or check the Appleseed website for events near you. Build a solid position and work on correct fundamentals before forming bad habits.
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Founding Charter Member - Middle Tennessee Shooter's Club