Lots of great advice already!
May is very much high season in much of Italy so time is of the essence to get accommodations booked; lots of folks have those wrapped up for 2025 high season already. I might suggest apartments over hotels so that you can all be together but you'll need to be cautious about what's advertised as a 'bed' as that might include a foldout in the living area. As well, you're going to want more than one bathroom. On the plus side, an apartment would provide the ability to have easy breakfasts "in" with supplies from a market.
Apartments are usually better for longer-term stays versus, say, one or two nighters to spread the cleaning fees over more nights. One drawback is not being able to store your luggage as you usually can when arriving at a hotel before check-in.
Car versus train: For your itinerary, definitely trains. You do want or need a car in Rome nor drive and try to deal with parking in the Naples/Amalfi Coast region.
Guides: that's very much up to personal preference and/or budget. My husband and I tend to prefer to explore on our own when possible although that involves lots of dedicated research. It can also depend on the place/venue and how complex it might be to do solo. in any case, if not booking a tour you're going to need advance, timed-entry tickets to the most visited attractions in Rome, specifically Colosseum, Vatican museums and Borghese Gallery, if any/all of those 3 are on your list. They're going to sell very quickly once available so be ready to jump on them when that happens, and you have the added challenge of needing 5 tickets.
A note about Rome: you could very, very easily spend the entire week there without running out of things to do. It's not clear if your two weeks includes the travel days on each end so it's possible that you'll realistically have 12 full days or less on the ground In Italy, and you'll lose at least part of a day in transfer to Campania. So, go easy on planning day trips? Orvieto is fine but IMHO, Assisi and Monte Cassino are too far.
I wouldn't call the Naples/Sorrentine/Amalfi Coast area 'laid back" either. it's going to be very busy in May so unless planning just to hang out at a hotel pool or whatnot, you'll find transport around the region to be packed. Ferries are a fun way to get around the AC- but tickets won't be inexpensive for 5. As an example, tickets for Sorrento> Capri, one way, are currently running a minimum of € 18,90 pp. SITA buses (which of course you couldn't use for Capri) are much less expensive but boarding lines can be long in certain locations and you'll be trying to keep 5 people together. I have terrible motion sickness too so ferries work better for me than road transport.
Circumvesuviana commuter train is also inexpensive - can use for trips between Naples, Pompeii and Sorrento - but is a battered unlovely thing with no creature comforts. It works fine but may be crowded and hot, and you'll want a tight hand on your valuables but that applies to virtually ALL public transit anywhere at all.
Monte Cassino: if you do try and do it - maybe from Naples as suggested - the website for the abbey states this (translated from Italian) if arriving in Cassino by train.
"A bus that leaves from the (Cassino) train station at 10:00, 12:35 and 15:20 (indicative time)
He then leaves the monastery at 10:20, 12:50 and 17:10. Check the departure times from the terminus at this link Autolinee Mastrantoni"
https://abbaziamontecassino.it/visita-montecassino/come-raggiungerci/