6) Bus option - X26 bus from Heathrow to East Croydon
This is the cheapest option, costing £4.50 off peak (£6.70 peak hours) using contactless payment, but it's cheap for a reason! It's a long bus journey, the bus is not going to be very comfortable, it's slow and you have several changes to make between bus and train. The bus fare is £1.50, the rest is the rail fare between East Croydon and Gatwick. From T3 to LGW isn't so bad, since the bus stop is at the nearby Heathrow Central bus station, above the tube station. Peak hours relate to the train service, not the bus component of the fare, which is £1.50 throughout the day.
The bus route runs from Heathrow Central Bus Station (stop 19) to Hatton Cross, then around south London to East Croydon (change for LGW trains) and on to West Croydon. From T5 you need to take the free tube service to Terminal 2 / 3 and the central bus station.
See TFL website for the timetable.
https://tfl.gov.uk/modes/buses/