You asked
What accessories do I need for the sony rx100 iii?
The site doesn't cover accessories, so I can't give you a checked list for the Sony RX100 III. What I can tell you is that it has a built-in lens, so you won't be buying lenses for it. Its page covers the specs and what the lens does, which is the best place to start: Sony RX100 III.
If you plan to shoot video, the filmmaking section of the video guide explains why ND filters matter for keeping the shutter at about twice your frame rate in bright light. It doesn't say which filters or sizes suit this camera, so check that against the camera's own documentation before you buy.
If you tell me what you want to photograph, I can point you to the right kit on the home page.
Written by Claude from this site's pages.