Once again: is it a 1.6 or 1.8?
Can you arrange for another transmission to go with this engine? The engine is more or less useless without the tranny.
Regarding your flywheel. Taking weight of the existing flywheel compromises its structural strength and integrity; light flywheels are usually made of stronger material to compensate for the reduction in weight.
I would suggest keeping everything stock initially and then upgrade in phases. That way its easier to troubleshoot and secondly you have a better understanding of how the car reacts to specific mods.
The JZ is a great engine, but its heavy, very heavy and I would probably throw the perfect 50/50 distribution of the bimmer out of balance. It might be a difficult task to compensate for that; so like I said, unless your drag racing you might want to do the minimum required first and assess how the car behaves before you spend more time on it.