If it were me, I'd take it ALL apart (and I did on mine) .... but I'm kind of anal like that
That way, you can cover the parts completely in paint. If you are doing a ground up, might as well go all the way. Plus there aren't THAT many parts anyway. Are you going with a stock suspension?...... air bags?.......... Are you modifying the frame/suspension at all? Like c-notching? If so, do all that stuff before you get your frame nice and clean. I had my frame all nice and pretty with a 4x6 drop then decided to go with air bags and ended scratching up the frame so much I had to repaint it. Just try to plan ahead to avoid stuff like that.