For watching a scene, it would probably be fairly normal clothes- shorts and a t-shirt, or boots, stretch leggings and a casual top, etc. An appropriate costume for the scene, such as a Jungle Explorer outfit, works too.
For myself, nylon swim shorts are good for hot weather, and my chest waders for cold weather sinks. I occasionally give in to nostalgia, and go mudding in jeans and my knee-high "barn boots."
I will probably lose some serious "man cred" for the following, but: I have worn pantyhose and stretch leggings into the mud.
It started because I really didn't want to have leeches on me, or any other nasty critters, especially on certain sensitive portions of my anatomy. I am tough and manly enough to burn the little blighters off with a lit cigarette- I would just prefer it not come to that. So, when I found a swampy bog that I'd be able to go more than thigh-deep in, I got pair of double-queen pantyhose to wear. Wow. They actually feel pretty good. And when there's nothing else between you and the mud, that feels even better.

Later on, my Lady Wife got a pair of stretch leggings at a certain unnamed discount retailer that didn't survive the first washing- they shrank until they were Capris on her, too tight, and the waistband started to unravel. So I grabbed those for my next outing.