Here is something you may want to consider. The ammo savings by shooting a .22LR will eventually pay for the .22LR firearm. You can work on the fundamentals, proper shooting form and accuracy shooting a .22LR. You should still practice with your centerfire firearm, but you don't need to fire it all the time. Also be aware that most .22LR firearms should not be dryfired - some can but most should not.
Proper shooting form and techniques help a lot for accuracy. I would look for a club that has Certified Instructors, RSO's or well experienced shooters willing to assist other members. Not all instructors charge a fee, but some do. Know in advance if there will be any fees.
Todd Jarrett uses and teaches some very sound fundamentals and shooting techniques. Here is one clip of him on the fundamentals.