Pompeii - Where to stay over one night

Continue on to Salerno and spend the night there.

Do you mean that you are visiting something other than the massive excavation site in Pompeii? Or is there something else to see there that you have learned about? Pompeii Scavi has excellent bag checking, but there isn't much else at that exact location. (I use the term Pompeii "excavation" to distinguish it from modern Pompeii, which has three stops on the Trenitalia line to Salerno.) I understand that the back entrance to Pompeii Scavi is a 15-minute walk from the Trenitalia line. But the Porta Marina entrance to Pompeii Scavi is 30 seconds from the Circumvesuviana commuter rail station. Obviously, you would not check your luggage at the Porta Marina entrance if you are planning to exit from the entrance nearer the Trenitalia stops. See next paragraph:

Note that your OP is not detailed enough. Have you booked a Trenitalia ticket to MODERN Pompeii? Or are you going to Naples and changing to the local commuter train product? Most posters here do that, but they're not going on to Scilla. Big difference, especially depending on your next rail link.

You have not stated whether your train the next day leaves from Salerno or where? I personally would book a hotel/train in Naples because it is more interesting than Salerno. Most importantly, Pompeii Scavi is well-connected to Naples (as well as to Sorrento.) But it is not well-connected to, say, Salerno. You even have the option of dropping your luggage in the hotel bag room in Naples then. But no one here has ever posted a complaint about the Pompeii bag check service! Well, maybe about high season lines, but that won't be your problem in April. Do prepare for sun and warmth, as well as possible rain.

Note that Pompeii Scavi has single-admission tickets and three-day tickets that allow admission to five ancient sites in the immediate (but very non-adjacent ... ) area. Only ONE admission is available to each excavation. But Pompeii (the big Scavi) has plenty of food options at the central cafe building inside the excavation. The others do not.

If you are going from Rome to Naples to Pompeii, the simplest thing to do would be to check your bags at the rail station in Naples, visit the ruins and then return to Naples for the night. Next morning, take the train to Scilla. I would not stay in either Sorrento or Salerno because it would not be convenient.

Trains departing Naples for Scilla stop in Salerno, so both Naples and Salerno are overnight options. Those trains generally don't stop at the Pompei (new town) station, so overnighting in Pompeii area wouldn't be a good choice. Sorrento isn't anywhere near the Trenitalia railway lines, so it's also not a good choice.

Travel Rome-Pompei. Taxi, Pompei to Pompeii villa dei Misteri entrance, Please note the difference in spelling, 5 minutes about € 6.
Check luggage at the entrance.
Taxi back to Pompei station and on to Salerno, 44 minutes. .
Staying around the station eases your transition the next day to Scilla.

Thank you for your helpful responses. I haven't purchased any train tickets, yet. I just have this plan to take a train from Rome to Pompeii, see the main Pompeii ruins for a few hours, and then get on a train to a good destination to stay overnight before getting on the train, again the next day, and head to Scilla. Hope this helps clarify. The consensus so far seems to be to stay overnight in Solerno.

Sorrento and/or Capri