If the engine and trans, is a straight bolt in job, of course paint the engine bay first. But if some modifications are required such as new engine or trans. mounts, or some other modifications to the firewall or inner fenders, it would be better to install everything first to make sure everything fits, then take it all out to paint. As for the body, it would depend on if the car needs to be moved around much to do the body and painting.It would be a lot easier to move under it's own power, rather than pushing it.