A cheap bike will be fine, infact if it has steel front forks it will have stronger dropouts to hold the motor in place, or like wise, steel frame = stronger steel frame axle. A cheaply made light weight bike will have very soft aluminium based frame and forks. Once you put a motor and battery on the bike, saving a few kg's on a lighter bike will probably make no difference whats so ever. As for regen, the ones with the kit serve their purpose pretty well as the main braking power if set quite strong to about 70%, but if you really want them for the purpose of improving your riding range they leave a lot to be desired. they will only get back a very small percent of battery power. you'd probably have to set them to 100% through the software and then have plenty of big hills to go down whilst braking in order to get a significant improvement in range. But saying that, I have no measurable proof, so I could be talking nonsense
