You need to enable HTTPS on the web server. To get the certificate you need to provide credentials and the host name of the server to a certificate authority (CA) like VeriSign or Thawte. They can provide you with a server certificate signed by their root certificate or some intermediate certificate. This certificate must then be imported into the web server to enable HTTPS over SSL. The web clients, like a browser or webstart will then verify the certificate chain when accessing the server.
If you use a self signed jar, all your users will be presented with a warning message about potentially unsafe code. To avoid this you should get a code signing certificate from a CA, which would be somewhat similar to the web server certificate. This CA-provided certificate can be imported into the keystore and used in the same way you use the self signed certificate. The code signing certificate will be signed by the CA so that the certificate chain can be verified by webstart.