What's the best and cheapest ticket to get? A Oyster Zone 1-6 and then an overground for the rest of the route?
Cheapest is unlikely to be the same as best, if best means most convenient/fastest.
island has made a good suggestion for the cheapest route, though it will take longer than travelling via central London.
Most convenient will probably be taking the Tube to Victoria (or train to Paddington and then Tube, or better 36/436 bus to Victoria), then taking an overground train to Gatwick. You can do this on one ticket and this will be cheaper than buying a separate Oyster and Zone 6 - Gatwick ticket. A Gatwick-Zones 1-6 Travelcard is £105.70 (
Any Permitted) or £92.60 (
Southern Only). Both Southern and Gatwick Express* run regular fast trains between Victoria and Gatwick, taking around half an hour.
There is also a £81.00
Thameslink Only Travelcard - Thameslink operate trains to Gatwick from London Bridge and St Pancras - the latter may be convenient from Paddington as it's an easy journey by Tube. Bear in mind that there is a lot of engineering on this route at the moment.
All of these tickets include unlimited travel within zones 1-6 (by any train company, as well as bus/tube etc). To look them up on National Rail Enquiries you need to enter Gatwick as the origin station, as it doesn't work the other way round.
*there is a long running debate here as to whether Gatwick Express is a genuine train operating company or just a brand of Southern - expect trouble if you use a "Southern Only" ticket on a GatEx train though.