Did the firemen, trimmers, stokers, and engineers have certain uniforms they had to wear or did they bring their own clothes? I researched in the bodies found of stokers and they don't seem to all wear the same color clothing.
No uniforms as far as I know. The fireroom wasn't the sort of environment anybody would have wanted one in anyway. Coal is unbelievably dirty stuff to handle so you would want to wear something that was as cheap and as expendable as possible.
As far as I know, very little has changed since then. Even with fuel oil firing, the mainspaces are sufficiently nasty places that coveralls are common, even in the Navy.
The firemen, who worked in a very hot environment, were very lightly clad when working. It was remarked by several passengers who encountered them on the boat deck or in the boats that they more than anyone else were suffering from the cold. Beesley, for instance, recalled of one man in boat 13: "He was clad at the time of the collision, he said, in trousers and singlet, both very thin on account of the intense heat in the stoke-hole; and although he had added a short jacket later, his teeth were chattering with the cold." There are accounts of stokers wearing (long) cotton shorts rather than full-length trousers. Whatever, this clothing would have been part of each man's own kit, not supplied by WSL and with no requirements for standardisation. This, and the fact that most of the firemen would not have been working at the time of the collision, explains the variety of clothing found on the bodies.
Rank & file crew members working in the engine room (greasers etc) were probably dressed like the deckhands in the same kind of everyday clothing worn by working men ashore, but without need for the heavy jumpers or uniform caps favoured in the colder working environment on deck. Some might have provided themselves with overalls.
Senior engineer officers on watch would have worn full uniform similar to that of the deck officers. A junior, more likely to be working hands-on, would most likely be wearing a boiler suit with maybe a jacket on top, and always with his officer's cap as a visible sign of authority.