I'm not sure what particular aspect of the long gun you are interested in, but you should definitely check out the appleseed program, its one of the best rifle marksmanship programs on the block, and a great deal for the money.
Neshooters is running a 2 day intro shotgun class on October 17 and 18, 2009, at Pelham Fish & Game. The course is being taught by Scott Reidy. Scott is a police officer, a nice guy and a hell of a shooter. He also teaches at Sigarms. We consider ourselves very lucky to be able to afer him as an instructor
For info on the course, please go to: http://www.neshooters.com/2009/reidy.html
NRA Basic Rifle Instructors will typically have a selection of .22 rifles that they teach the class with, and you should be able to get familiar with at least lever action, bolt action, and semi-auto, if not also hinge action and pump action.
It's not designed as an opportunity to demo rifles outside of that. It's designed to teach basic skills. What I mean is that it would be unlikely that you would come across "big boy" rifles in a Basic Rifle class.
There will likely be some NRA Basic Rifle courses at Bass Pro coming in the late spring/early summer, so check in there as the spring rolls on