One of the great things about selling postcards on eBay is that they are incredibly easy to ship, as long as you have a few simple supplies on hand. The first item is a postcard sleeve for use in protecting the card. These are the two most popular sizes, and even in small quantities, they are very reasonably priced.
The next item that makes shipping postcards easy is a rigid mailing envelope. It still is slightly flexible due to it's light weight, but it protects postcards very well. It also typically ships based on a postage rate based on about 2 ounces. The rigid mailers I recommend measure 6" x 8" and can hold either popular size postcard. These mailers also can easily handle a multi-card order.
The last easy item to use for mailing postcards is simply a "Do Not Bend" label. It shows that you care about how the order arrives to your buyer. Typically I use two of these labels on the mailer. One on the front and one on the back.
This way of shipping postcards has served me well for a number of years. It works great with the eBay requirement of tracking for your shipments. There are definitely other methods that will work for you, but I've found this one is simple, very easy to keep on hand and breaks down to a small cost per postcard shipped.