The direct train is the Circumvesuviana from Napoli Garibaldi toward Sorrento. The stop is Pompei Scavi–Villa dei Misteri, not the mainline Pompei station, which leaves you in the modern town. The ride is on the order of half an hour to forty minutes. Check the day’s timetable. A late train does not move your entry.
From the platform to the gate
The Scavi station is a short walk from Porta Marina and Piazza Esedra. You do not need a car for a morning in the city. You do need the named ticket before you join the line, unless you are prepared to buy at the window and accept whatever the day’s cap still allows. We buy the official ticket in your name so that question is settled before you leave Naples.
If you want more than the city
Villa of the Mysteries is the add-on people mean when they say the villas. It is outside the city walls and it is not in the €20 ticket. Herculaneum is a different site again, with its own ticket, and it is not Pompeii. Say in the note if the day should include the suburban route. We will quote that ticket instead of the city-only one. The first Sunday is still free at the gate, and we still will not sell it.