If you're flying intercontinentally, then yes, LGW is the easiest. From LHR you can, however, get the RailAir bus to Woking, and pick up the train direct to Salisbury from there.

Domestically or intra-European, then SOU is by far the easiest, as there are direct trains from the airport to Salisbury (and it's closer than London).

A final option is BRS (I believe there is an EWR-BRS on CO) - there are direct trains from Bristol Temple Meads to Salisbury (the airport is a bus ride from the station, though, unlike SOU).