Train from Rome to Pompeii (or to Naples)

I prefer

https://www.trenitalia.com/content/tcom/en.html

You will be taking the Circumvesuviana local train to Pompeii from Naples
No advance purchase/booking it’s like a metro

https://www.positano.com/en/naples-to-sorrento-train-schedule?timetable_route=napoli_sorrento

Search this forum for “Circumvesuviana” for more details how to catch it

Circumvesuvian schedules here.

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

Buy the tickets directly from the train company - either Trenitalia or Italo for travel between Rome and Naples. The train from Naples to the Pompeii excavation is an entirely different company - Unica Campania's Circumvesuviana - that you can not get from Rome. Depending on when you are going, you could take the tourist version (Campania Express) that is faster and air conditioned, but it doesn't run all year and doesn't run as frequently as the commuter version of the same train.

Do verify exactly what you mean by "scavi station." Do you mean Circumvesuviana train station "Pompeii Scavi-Villa Mistiri?"

Aren't there two stations in Pompei? The Circumvesuviana one near the Marina Gate, and the Italo/Trenitalia one further about a mile to the east & a few blocks south of the Amphiteatre gate? I think this is getting to OP's question.

Trenitalia does have a train station in the modern city of Pompei (spelled with just one letter "I"). But it's not served by the fastest trains from Rome, so it still requires a regional train connection at Naples (or Salerno) and then you'd probably also need a taxi or city bus to get to your hotel - versus it sounds like your hotel would be an easier walk from the Pompeii Scavi station if you take the Cirumcumvesuviana line.

There is at least one hotel between the Porta Marina entrance and the Villa Mistiri gate. But there is nothing else to do there. I would not bother to stay at/in Pompei unless I was doing two days in the ancient city for some reason. I'd stay in Sorrento or Naples and have something to do in the evening.