The cheapest way to get classic parts is to find them yourself. This means taking a road trip, putting on your work boots and tool belt, and wandering around the junkyard in search of that diamond in the rough.
The most important rule of junkyard salvage is to know what you're looking for. If you don't, skip it. Also, once you find the rusting frame of your dream car, you'll need the skills to evaluate what's classic and what's junk. The salvage yard is not the place for the inexperienced. That said, it might be the perfect place for the expert.