I bought the bike I started with at a flea market for $25...many others here have found suitable bikes for less. If it were me, I would just get a bike I knew would fit the engine...for me, the engine is more important, and I build around that. You may even find a frame that can use components from your current bike if you are interested in that.
The Grubee Skyhawk (Stage II or III, I have the II) is the gearbox. I have the gearbox on a Honda and many, most, people have the Huasheng engine...which is a pretty good engine from what I hear.