I have only been to STN once before (last week), although I will be there again later this week. I would leave for STN at least three hours before my flight.
I would take the Piccadilly Line one stop to Holborn and the Central Line to Liverpool Station. The tube is always a possible cause of delay. I am allowing for a half hour on the tube. The Stansted Express leaves every 15 or 30 minutes to the airport depending on the time and the day of the week and takes about 45 minutes.