Oh, not to confuse you more...but there are great double surface trainers. The Pulse 10m comes to mind and would be perfect for your size. I've flown a new one, super easy wing. I spent quite a bit of time on top the stack at Elsinore on a ridge day on my demo Pulse. They are back in production by Northwing. Simple design, No VG, and a straightforward setup.
Bring it up with your instructor. That said, you can't lose with a Falcon, but at some point, yes, you are likely going to want a DS wing.
Welcome to the sport, btw.