Rome to Pompeii advice

High speed train from Roma Termini to Napoli Centrale.
http://www.trenitalia.com/
At Napoli Centrale look for signs to Circumvesuviana.
http://www.eavsrl.it/web/en
Buy tickets for Circumvesuviana train at ticket window, walk downstairs (trains are underground level) and look for train to Sorrento. Pompei-Villa dei Misteri station is half way between Naples and Sorrento.
You can leave luggage at the station or at the Archeological site. It's a guarded storage facility that works like a cloak room at a theater, it's not a luggage locker.
Later retrieve your luggage, walk to the station and proceed with another train to Sorrento.
Private driver and guide from Naples is also possible, but more expensive.

Since there are six of you, it might be worth it to have a car service/guide and take some pressure off yourself.

I wouldn't stop along the way. I'd go straight to Sorrento, drop your bags, get acclimated, tour Sorrento, and then leave Pompeii for the following day. You'll need to budget about a half day (or more or less depending on your group's interests) for Pompeii anyway. Not having luggage with you will take care of at least some of your worry. And you'll hopefully be relaxed first thing in the AM.

If there are 6 of you, then maybe it's worth paying for a tour or car service that you can split. I don't have any advice on that since I often travel alone or with a friend or loved one.

Here's some info hopefully you can use:
https://www.rometoolkit.com/naples_visit/naples_circumvesuviana_trains.html

We visited Pompeii from Sorrento, and I also recommend that. However, vast numbers of posters here use the luggage check COUNTER (not lockers I think, this is right beside the ticket counter for Pompeii the ancient city) and in two years I've never read about ANY problems. You do need to know that the Circumvesuviana is typically very crowded and hot, and you will have real trouble getting your luggage on and near you. (Fuggeddabout racks, it's a commuter train.) That's another reason you don't want to stop at Pompeii (which is right beside the station at Pompeii Scavi, only a 50 meter walk.)

Six people won't fit in a sedan with their luggage, so you'd need a premium vehicle. The Circumvesuviana is very cheap, so it's hard to beat for either Sorrento or Pompeii. Because we needed a cab locally on our departure from Sorrento, we splurged 90 Euros on a Mercedes sedan and driver back to the Naples rail station. If you have discount (Rome-Naples) tickets, remember that they probably are for a single departure and not changeable. Same day tickets are flexible.

Don't forget to validate your tickets in the machine before boarding the Circumvesuviana.

Thank you for your reply. Did you go to your hotel and back to Pompeii on the same day?

Oh, no. We slept five nights in Sorrento specifically because it is an excellent transit hub. I personally find it to be a postwar, reinforced concrete resort product, if attractive, heavily patronized by British sun-seekers. The next question you are going to ask me has the answer,

We paid our luxury hotel's car service partner 240 Euros for eight hours of Mercedes and driver to see Positano, Amalfi, and Ravello (with some other stops) from Sorrento and home to Sorrento. We don't have budget problems, but we also had no desire to do this driving, waiting, and parking ourselves.

One of our nicest excursions was the 2.4Euro (?) local bus to Sant' Agata on the hill, and a 1.5 hour, 99% paved steep walk downhill back to Sorrento. But this cannot compare with [what I read about .... ...... ] the steep hill walks on the Amalfi Coast.

We did Pompeii one day, and Herculaneum and Villa Oplontis another. But that is overkill for 99% of visitors. I'm not urging you to buy the 3-day, five site Pompeii ticket! We did not have time for Capri, but most people would say that's a must. Having just been to Capri from a cruise ship last month, I don't think it's an absolute "must." For example, the Aeolian Islands were far more attractive than Capri.

We did the Rome to Sorrento trip with a stop in Pompeii and back to Rome in a day with no problem.

Earliest high speed train to Naples - then the Circumvesuviana (watch the sign boards for the right train) to Pompeii.

We then continued onto Sorrento for a walk around and nice lunch, back to Naples Station and return to Rome about 8pm

I DO suggest at Naples you buy tickets for each leg of the Circumvesuviana you want for each person - tickets are cheap - however returning out of Sorrento there was a problem with the ticket machines inside the booth and we almost did not make our train. If we had bought each leg in advance at Naples we could have avoided this.

For instance we should have purchased at Naples:

1). Naples to Pompeii
2). Pompeii to Sorrento
3),. Sorrento to Naples

This way we could have been all set with 3 tickets each in our pocket from the start and avoided any more ticket booths. Next time this is what we will do. The Circumvesuviana ticket purchases are not automated. You buy from a person at a control booth.

For us the worst would be we stayed in Sorrento overnight - however for others on a rigid schedule or budget this could be problematic. Others have said the Circumvesuviana was packed, we did not experience this - I mean it was full from time to time however most of the time it was perfectly fine and nothing like the Rome metro.

In addition to the regular Circumvesuviana commuter between Naples and Sorrento, there is an express 'tourist' train that makes fewer stops. It costs a few euros more and has less frequent runs but will get you there more quickly, and looks to be more comfortable than the standard, bare-bones commuter.

http://www.napoliunplugged.com/campania-express-tourist-train-to-herculaneum-pompeii-and-sorrento

http://www.eavsrl.it/web/sites/default/files/eavferro/CAMPANIA%20EXPRESS%202016.pdf
("A" means arrival, and "P" means departure ( arrivi and partenze, in Italian)

Do note the months it doesn't run should your visit be during the winter season.

Thank you everyone for your replies. Very helpful!