The original Gate production of 1996 essentially had a bare stage, while the action took place around some of the audience (there were seats in the middle of the auditorium). Much of the action was in the main stage area at the far end of the auditorium, but the Doctor's conversation with Phaedra was held in a side aisle, the Hippolytus/Priest scene at the near end, and the lynch mob gathered all around the whole auditorium - they threw each other Hippolytus' dismembered organs over the heads of the people sitting in the middle sections.
The only props were the ones called for by the script - eg Hippolytus' telly and pile of unopened birthday presents lying around him; the barbecue for the lynching scene - and a laptop, which Strophe used in the scene where she is described as working.
The cast wore ordinary modern clothes - Hippolytus a jumper and trousers; Phaedra a low-cut dress; Strophe a businesslike jumper and skirt; the single actor playing the Doctor, the Priest and Theseus a black shirt and trousers (adding a dog collar for the Priest and, I think, a white coat for Doctor); the policemen modern riot police uniform.