Southern Rail's off-peak fare is £13.20 each way (cheaper than Gatwick Express and takes only 6 minutes more).
Easybus goes to/from Earls Court and takes twice as long, plus the time to and from Earls Court/West Brompton tube station.
Gatwick Express is rubbish! - the trains they use these days are not designed for people with luggage etc. Southern will be cheaper and better.Check National Rail web site for journey times. On Sunday services start later.
Any train operator will sell you an advance ticket with any train company.
You dont have to go to (for example) Southern Trains to buy a Southern trains ticket.