The problem with painting the entire helmet red is that white often allows colors (like red) to show through the white layers similar to a "bleeding" effect. By creating a white "undercoat" you'll be able to have the red "pop" better. I would personally shy away from painting the "detail" colors as the base coat and using later coats to do the base of the piece. I may be off, but I'd say most people prefer this method. It also makes this easier to create weathering and battle damage on the detail paint.
Although taping the details for painting would work well, I would also suggest looking into creating your own water slide or inkjet printed decals. I don't know how detailed you want the helmet to be, but those are all good ideas to consider.