I need to connect PEX water pipe to the end of an outside water valve and would like to use either a sharkbite or gatorbite connector. What am I looking for when buying the connector?
The connector has to swivel to be able to remove it and reconnect it to the valve. What number should I be looking at for this 1/2" x 3/4" connection?

Are you asking what kind of thread does a hose bib have? If so, its is a hose thread, its not any kind of pipe thread. Only thing that will screw on is a hose. Doubt that you will be able to attach a hose end to Pex.