Your payment, shipping and zones set-up is probably incomplete. You need to assign zones to the shipping module(s) you've activated.
ZC bases things like payment options, tax calculations and shipping methods on the customer's address (you can alter this in admin).
Before ZC can "calculate" what payment methods, taxes to apply (if applicable), or what shipping method to offer a customer, it needs to know the customer's address relative to the zone settings you have configured.
(In your chosen payment modules, make sure you have set the zone to either "none" (which allows that payment method to be used by anyone in the world), or to your defined zones (limiting who may use it, depending on where they live).