What do court reporters suppose to wear?

"Respectable". If you're a woman, a nice conservative outfit; dress, skirt or slacks are ok, as long as they are not jeans (unless they are dark with no embellishments). No low cut blouses, or...

A suit, or nice slacks and button down shirt with collar. A blazer jacket over that would be preferred. The way one dresses is to show respect for the court. No personalised items, such as logo...

to inform the public of what is happing during the trial.

The US Supreme Court doesn't use a standard court reporter, as trial courts do. The position most analogous is the Reporter of Decisions, who is responsible for ensuring oral arguments are recorded...

What a bailiff wears depends on the court. Bailiffs are law enforcement officers assigned to protect a court. In California trial courts, Bailiffs are nearly always county Deputy Sheriffs and they...