I've had rainbow hair once, though it was just my under-body.
I'm just going to say one thing - pulling off rainbow (or any sectioned hair design) is no easy task. The wrong dye, shampoo, or improper sectioning can cause the colors to bleed into each other (this is coming from experience from the first time I had my hair dyed, it honestly looked awful.) Some colors (orange and yellow especially) don't retain well when applied, so bleaching before dying might help the colors be more vibrant and last longer.
Making sure it stays rainbow after it's been dyed is also not a simple task. Initially when you run water over it some of the dye is going to come out, though you'll have to be extra careful to not have the colors bleed into one another. The best way to do this would be to put your head down, section out each colored section, and lightly strain the water out of it. Time consuming, but the result will be worth it.
Yet again I'm sure the person you have dying your hair will tell you all about caring for it when it's done.
G'luck. (':