Talk about airplanes! At last count, there are 39 (and growing) FAA certificated S-LSA (special light sport aircraft). These are factory-built ready to fly airplanes. If you can't afford a factory-built LSA, consider buying an E-LSA kit (experimental LSA - up to 99% complete).
What if you have an S-LSA and re-register it as E-LSA. Then, as an experimental LSA, where do you think you might be parked at Oshkosh when you fly in?