Gatwick Express is actually part of Southern Railway, though it retains its separate identity. Gatwick Express services run every 15 minutes all day between Gatwick Airport and London Victoria, taking just 30 minutes for the non-stop journey.
As such, it's the fastest way to travel from Gatwick Airport to London, though it's also the most expensive - both Southern and First Capital Connect have cheaper train fares, though these are, of course, on slower services.
However, if you have lots of luggage (Gatwick Express services are generously provided for with lots of luggage space - in marked contrast to many other British train services), need to get to London quickly, or want a more relaxing journey, then Gatwick Express is probably the choice for you. Buy train tickets with MyTrainTicket - whether Standard or First Class, both are available.