The backbone needs to twist around for each strand to make the double helix, alternating in colour for sugar and phosphate, and running in opposite directions (one strand has a phosphate at the top and a sugar at the bottom, the other strand has a sugar at the top and a base at the bottom). Within the helix is a parallel "ladder" of base pairs, either coloured for each of the four bases or each of the four pairs. I would use related colours for the two purines (dark and light green, say), and for the two pyrimidines.
I agree strongly with
@Eagle Mum that making a model from just plasticine would be very difficult, though it depends how simplified it is. For example, could the base pairs be toothpicks covered in two colours of plasticine, a larger length for the purine and a smaller for the pyrimidine? These could then stick into the helix shown as a ribbon of alternating colours (one base pair coming off each sugar). Just a thought.