A sturdy tripod is really an essential, although good pictures can be made taking advantage of walls or rocks etc on which you can place your camera. You will also need a cable release which has a lock on it to hold the shutter open. Medium speed or slow film is often the best to use - even a fast film will need long exposures on a tripod, and you may as well use even longer exposures and get the extra quality a slower film provides. Films differ in their responses to long exposures, but all suffer from an effect known as reciprocity failure . These will differ from emulsion to emulsion, but there are often fairly clear trends by manufacturer.
Some films are definitely less affected than others.
If you want to use colour, transparency film is generally a better choice as the reciprocity failure in negative films causes problems for most laboratories in making prints, and results are unlikely to be satisfactory. Most films are made to give proper colours in normal daylight, although a few are produced for use with studio tungsten lighting. These will normally give better results when taking pictures using street lighting, but for moonlight it is more a matter of personal preference that you will need to find by experiment. I suggest you start by using your normal favourite film. Unless you work within a few days either side of the full moon, exposures may extend into hours rather than minutes.