The script for "South Pacific" shows the musical has several different sets, including the CO's office, a South Seas plantation, a big Navy party and the island of Bali Hai. Items that belong in these sets, such as Tiki torches, military radios and coconuts, belong on your list of possible props.
The characters in South Pacific---including naive Nellie, her lover Emile and Bloody Mary---are often described using props. Some are ordinary, such as drinking glasses, and some are more distinctive, such as Bloody Mary's cart of items for sale or the shower Nellie uses while singing "Gonna Wash That Man Right Out Of My Hair." Those items go on the props list along with items that aren't mentioned, but you think would enhance the scene.
Your director or producer will have their own ideas about what they want on stage in "South Pacific" and what props they want the actors to use. Their suggestions go on the list. The producer will also review your ideas and see if they're affordable and whether some of the props are really the responsibility of the set builder or decorator.
If your theater company has been around a while, it will have a props closet you can search for ready-made items you can use in "South Pacific." Other sources for affordable props include anything members of the cast and crew might have at home, such as an old radio, anything local businesses might be willing to donate or loan for the musical and anything the tech crew can build cheaply. Prop-rental companies are a lot more expensive.