People venture into the world of being a DJ and don't ask questions because somewhere along the way someone made them feel as though they asked a stupid question. There are no stupid questions. Either you know or you don't know.
Is it my right or the audience's right?
It's your right. Red is your right and white is your left. You're facing the audience and the white RCA cable goes to your left. If you are just hooking up RCA cables from turntable to mixer then it is clearly marked on the gear R and L or + and -. In some rare occasions you might find yourself using an old piece of gear that has the writing rubbed off. It should clearly have the coloration of white or red inside the inputs. If you put red in white and mix up the wiring you will get crappy sound.
Should you buy gold plated RCA cables?
Yes. They sound better. Is anyone really going to know the difference if you don't? Not really.
Most people are afraid to ask about RCA cables because most DJs act as if everyone should magically know about RCA cables. The subject isn't very complicated. Red/White, Right/Left, Positive/Negative.
Common DJ variations of the RCA cable.
RCA to RCA. This is what you would normally use to connect turntables to a mixer.