A WAP Gateway is a specialised type of proxy server.
WAP clients connect to a WAP Gateway using UDP, on either port 9200 or 9201 (usually 9201, it depends on whether the phone is configured for connection-less/temporary or connection-oriented/permanent). Or, if WTLS encryption is used, port 9202 or 9203.
These port numbers are UDP ports, not TCP ports. (UDP is a connection-less protocol that is implemented on IP, TCP is a connection-oriented protocol that is implemented on IP.)
Any MIME types that are registered on a content server (WAP Server) are really independent of the WAP Gateway. Most WAP clients expect to see WML content in the MIME type "text/vnd.wap.wml", and monochrome images in the MIME type "image/vnd.wap.wbmp". However, newer clients that support XHTML Basic use "application/xhtml+xml", and regular image types like "image/gif" and "image/jpeg".
In most cases, when your operator has a WAP Gateway, you can connect to any WAP site on the public internet through their gateway. You generally will only need your own gateway for more specialised setups.