You can paint it when you want, better soon than later! :) Just because when the paint are drying you can work and complete the chassis.
Before assemble the body for paint it, be sure how the chassis goes attach with the body. I don't know, the Viper, I never build it, but some time the front or rear bumper goes kind of under the chassis (for keep the body and chassis together), so it require that the front or rear bumper need to be paint separately and put on the model a the end.
About the color, usually I use this method:
Primier, Color, Clear Gloss and Polish...
For each one I give 3 shots of paint.
1- A soft shot of color, kind of you still can see the plastic of the body
2- A medium shot, this one cover all.
3- The final shot.
After I use some polish and polish all... Usually I use Turtle Wax... :)