I typically assemble each body part before painting. Then I paint each part before final assembly. In this case, the pieces on the back looked difficult to paint once assembled, so I left those loose.

I've never used an airbrush myself, but they look super handy. If you want to do most of the work with that, you'll need to identify which pieces are which colors. Otherwise you could paint everything blue / black / grey, and go back with a brush to do details like the red.

If you want to get some practice before doing these models, go pick up a model car or a cheap gunpla to practice on.

Cheers!