You'll end up doing some of both.
The armor people often paint a mostly assembled model. The ship people tend to prepaint or paint large subassemblies.
Aircraft usually paint the detail parts separately, but paint the airframe after assembly.
Be aware that painted parts can only be assembled with solvent glue if the paint is removed from the gluing surfaces, This isn't hard, and solvent joints are very strong.
Otherwise, painted parts can be assembled with CA (superglue) but the joints are not as strong.