Azmark--If what you want is real rifle marksmanship basics, you oughta attend an Appleseed weekend event. Besides American history, rifle basics is what Appleseed is all about, and you get instruction, along with shooting (oh, lots and lots of shooting!)
An autoloading .22 with several 10-round box magazines, sling swivels--with military-style sling--and possibly a 'scope, is the ideal weapon for an Appleseed, along with abt. 500 rds. of ammo. But you bring what you got, and shoot what you brung, and the very-well-schooled instructors @ any Appleseed will work with you to bring out your rifle's best, and to greatly improve your own best shooting.
Appleseed events are held all over the country. Their website will let you know when/where there will be one near you. If you have to drive a little to get to the event, IMHO it will be well worth your time.
Good luck and please keep us posted!