cut, assemble, etc first
then wood fill - you WILL have small gaps here and there, and you use wood fill to make it all feel like 1 piece ... you sand that
prime (2 coats) - dont need to sand TOO smooth here
paint
this way you can fill all the small gaps, and paint over it all.
ALSO ... you may ding the paint while building/cutting/etc.. this way you dont have to worry about it while building
I personally only painted the visible parts.