Day trip to Naples

No need to buy tickets ahead of time but why not save time .
If your bag is to big for the cloak room you could leave here near the train station

https://www.stowyourbags.com/en/shop/naples/luggage-storage-naples-central-station/

Day trip from? Next stop after one site in Naples? Have you seen Pompeii?

Edit: This is a fine museum, and the Farnese Marbles are as nice as the Pompeii artifacts. But if you haven't been to Pompeii, I'd go there, and Pompeii has a fine bag check.

Where are you day tripping from?

There’s no need to buy tickets in advance for the museum. Easiest thing regarding luggage is to check it at the rail station. You will not be able to check them at the museum. But in all honesty, Naples deserves more time.

At the museum, there are several larger compartments, that might accommodate your bags - and you might need two. Since the lockers are free, there's no incentive to use the smaller ones, so I wouldn't count on empty lockers big enough for your bags unless you get there more or less when they open. I doubt there'll be a long line for tickets, you may have to wait 5-10 min for a group if your timing is unlucky.

It seems easier and worth a few euros to store the bags at the train station instead of shlepping them to/from the museum.

We are coming in from Capri via ferry and planned to go right to the museum. To go to the train station first seems inconvenient. If we can’t store our carryon sized bags at museum, can anyone advise another convenient option? I appreciate all of your insights.

I should say we are coming to Naples via ferry from Capri, then leaving from train to go to Rome.

The museum is a short metro ride from the train station and you'll have to return there anyway, so I don't think storing your luggage at the train station is as inconvenient as you might think. Sounds hit-or-miss as to whether the museum will be able to accomodate your bags, but I can't be sure as I've neither tried to store luggage there nor payed attention to those trying to do so. Hopefully someone will have a definite answer for you. What might be inconvenient is going directly from the port to the museum, finding out that can't accomodate your luggage, then having to go to the station and back. I've never had a problem buying tickets upon arrival at the museum.

Thank you. I may risk the museum. I’m kind of nervous. This is the one part of my plan I hadn’t quite worked out period I appreciate all of your ideas and have you given me much to think about.

The museum is one of the best in Italy. It's worth the hassle in my opinion. The best plan is to take a taxi from the port to the train station, stow your luggage, and then take another taxi to the museum. Also, before you go, download Rick's audio tour of the museum so that you have it on your smartphone (see https://www.ricksteves.com/watch-read-listen/audio/audio-tours/italy). If you lots of time after your visit, you can take Metro Line 2 back to the station--or if time is short, take a taxi back.

Thank you all for the responses. I'm wrapping up my plans and this is my only fearful part, mostly because I haven't gone to Naples before and it feels foreign. lol I think based on all of your insightful responses that I will take a cab from the port and go directly to Stow your bags. https://www.stowyourbags.com/en/shop/naples/luggage-storage-naples-central-station/
Has anyone used them before? I am assuming they will have available lockers and that they are safe, right? (Can you tell I'm nervous?)

Also, I'm hearing a lot about the safety of Naples. I have two young kids, just wanted reassurance that we can walk freely without too much concern. Thanks so much for all of your input!

Kath, statements about safety in Naples are colored by people who have never lived in a big city with a heterogeneous population and tight quarters and limited municipal budgets. That now describes almost every city, big and small, in the United States. We never felt the slightest fear in Naples, even though I did have a pickpocket-attempt in ROME many years ago. I can assure you that your physical safety is in much more danger in the U.S., even though no one wants to believe that. (We're over a hundred mass shootings for 2019 already.)

I noted this discussion here, but it may be more reading time than you want.
https://community.ricksteves.com/travel-forum/trip-reports/surviving-naples

Some other tips that might be of interest to you:
The Frecciarossa train service to Rome is very fast and comfortable, but has a high walk-up fare, if you don't buy months in advance. And it's non-changeable, non-refundable.
Don't overlook the Farnese Marbles in the Archaeology Museum. Consider whether your kids should go into the erotic fresco room.
Expect to wait in a substantial line for a Neapolitan pizza lunch table.
There is more to Naples than the Arch. Museum.
Buy the kids a Baba pastry from a street-front bakery.

Fixed taxi fares to Napoli Centrale and then to the Museum are €13, but you need to tell the drivers. Entering the station, Deposito Bagagli is straight ahead and to the left. Buy your Rome tickets from a machine after picking up your bags.

Rzollezi has given good advice. Take a taxi to Centrale and store your bags at the station. When you get ready to leave, you just go back to the rail station. Then you can get the Metro Line 1 from the station to Museo to visit the museum and return the same way. Very easy and fast.