A regular Taxi cab cab you just get in at the hotel would cost 100 pounds.
A Licensed Airport Transfer Private Car Services cost about 55-80 pounds.
National Express Coach Service bus will be about 20-25 pounds.
http://www.tripadvisor.com/Travel-g1...o.Gatwick.html
I would take the direct route bus and give yourself an hour extra in case of traffic. Look for the route that would have you arrive at your ideal time and add an hour to the bus departure time.
If you want more sleep, eat the cost and stay at Gatwick. The taxi or "limo" service fee difference would equal a cheap hotel at Gatwick.