What is the best way to get from the Naples Airport at 6:30 pm in August to Sorrento?
Most convenient is a car service, but that can set you back about 100€
Otherwise there is the Curreri bus shuttle
http://www.curreriviaggi.it/autolinee/images/AUTOLINEE_CURRERI.pdf
Otherwise bus or taxi to the Napoli station. Then Circumvesuviana commuter train to Sorrento.
Or bus/taxi to port then boat to Sorrento.
Roberto gives you all the options. If you can at all afford it, I'd encourage you to use the private driver. Not sure if you're going to be jet-lagged when you get to Naples, but if so, that's all the more reason to consider the private driver. My second choice would be the bus. Enjoy, Sorrento is beautiful!