Train Sorrento to Paestum or Pompeii/Herculaneum

There is no train from Sorrento to Paestum. You can take a bus to Salerno and transfer to a train or bus from there to Paestum. However, not sure how much time you will actually have in Paestum, given your 1.5 hour estimated time to/from your ship in Sorrento. By public transportation, Sorrento-Paestum is at least 3 hours each way.

This is one of those times to either arrange for a private tour or a ship excursion, if offered, for Paestum.

The Circumvesuviana runs from Sorrento to Ercolano (Herculaneum) and Pompeii on the same route.

In mid-August, lots of heat and crowds.

In August, I would pay whatever the cost for a private excursion, and probably to neither of your choices. Too hot for all that!

As stated above, I would forget Paestum. By bus, taxi or private transport, once you're on the road it's about 30 minutes to Pompeii, close to an hour to Ercolano.

I would set up in advance--if you can--a late lunch (14:00-14:30 res) in Sorrento. On your arrival at 9:00 at the port, hire private round trip transport to take you immediately to Pompeii, and hire a guide as well, either at the Porta Marina entrance or in advance. With a good guide, you can see the main highlights--nothing is marked--in 2.5 to 3 hours, maybe before the crowds & heat make you crazy. Then ride in the cool car back to Sorrento. Have a leisurely meal and wander the streets until it's time to go back on the ship. You'll spend money but it will be well worth it that time of year.

Are you certain that your ship will actually dock right in Sorrento? The biggest ones don't. Or is it a tender job?

Both Paestum and the scavi from Vesuvius are almost completely outside with negligible tree cover and in August will be scorching and tiring.

I have visited both (and Sorrento) in April and loved it. I'm not sure I would want to be there in August.

You must be coming into Sorrento on Oceania Riviera?

http://www.cruisemapper.com/ports/sorrento-port-1460?month=2017-08#schedule

You'd have to confirm with your cruise line but I believe that'll be a tendered port for your ship. Let's just say that a look about turned up multiple mentions of tendering from other cruisers who've had that port on their itinerary.

(edited to fix a typo)

Have you been on cruisecritic.com? You can find your cruise (under the Roll Call option). Veteran cruisers always start a thread for each cruise they're on. You will get valuable information on what options are available for every port stop including private tour operators. Veterans often organize small private tours that are both cheaper and more efficient than the ship's excursions and welcome others to sign up for them.

Unless you have mobility challenges, you could get to the Circumvesuviana station in 20 minutes from the tender dock.. But it requires planning and map printouts. August is indeed crowded and sweltering, so an air conditioned bus sounds worth 130 Euros per person, and no ship-time worries then. But Pomp and Herc are entirely practical on your own. Amalfi Coast might be cooler but only with the ship's tour due to road congestion.

In August, Herculaneum would be best as it has some shade, is very easy to navigate and do a self guided tour. I prefer it to Pompeii, much better preserved and it is still under active excavation, I see a bit more each time I visit!

Taking the cruise info website suggestion above seems logical. Enjoy!