I DO save my collars and cuffs. I cut around the stitching to save time ripping those seams...if the interfacing will tear off - I tear it off! If not I toss it and save the side that doesn't have interfacing. Before I even start scrapping my shirts I remove buttons with a seam ripper. This is actually my ten year old's favorite job to help with! Also - look for 75% off and 25 cent sales at thrift stores. My local Goodwill has them three or four times a month and you can walk out with a handful of shirts for a buck or two.
I also try to find shirts that don't look like some guys old flannel. I look specifically for shirts that look like reproduction civil war prints!