Sure...the airplanes are cheap, but good luck maintaining one. Fuel costs, inspections, AD compliances, storing, insuring etc etc. Dissasembling the airplane every year for the annual is a real hoot, not to mention paying the inspecting mechanic and fixing whats broken. $25,000 engine overhauls every 2000 hours. Then you still have things like landing fees.
Unless you're loaded, don't go it alone.
Oh, a private license is about $6000. You'll fly about 50 hrs.