Don't forget that whilst the Gatwick express is non-stop, it is quite expensive and often crowded. There are Southern Trains every 10-15 minutes or so which are cheaper, and take about 30 minutes to Clapham Junction or 40 to Victoria.
From Clapham you can take trains West to Chiswick, Hounslow, Feltham, Richmond etc every 15 minutes or so, or North on the Thameslink services through to Hampstead, St Albans Luton etc.
From Chiswick I can usually get to LGW in about 50mins via Clapham by train which is quicker than driving.