Do I set the shipping prices on my products?

No, there is no need. The shipping price charged to the customer is determined by Zazzle. Shipping prices are determined based on the dimensions and weight specified in the 'Fulfillment & Shipping' section, under 'Shipping Information', when adding a Customizer. In addition, the 'ship to' and 'ship from' address and the shipping speed are selected by the customer at check out.