I suggest you to try it in after effect. If I got right what you want to do, the plug-in Trapcode 3D Stroke might help you in making the rainbow-like thing. You can find more info about it here
As for the background, try something like this:
White solid layer, over this put the layer with the word "Productions" and over this a black solid layer. over these 3 layers you do the rainbow-like thing with the 3d stroke and when it's done, put a keyframe to the black solid layer's opacity. Then go to the point in time where word production must be fully visible on the white background and put another keyframe on the opacity of the black solid an put the opacity down to 0. This should work.
Also, at the trapcode site, there's a tutorial for the 3d stroke, so you can learn to use it, beside buying it (you can still download a trial edition, but there's the watermark).
Also, there might be some way to do the rainbow in Particle Illusion, but I prefer to stick to AE and plug-ins.