Pisa airport to Cinque Terre

Yes, Pisa Centrale is the correct station to use. You will get there by a quick connection on the airport's People Mover train. The Cinque Terre is a region of five towns, so specify the one town where you want to arrive: Monterosso, Vernazza, Corniglia, Manarola, or Riomaggiore. You will usually expect to make a connection at La Spezia Centrale station, but the schedule results will tell you that.

I was posting the same thing. CT is an area or region. Where exactly are you going in that area?

Monterosso
Can I purchase tickets when I arrrive? Sometimes flights have delays & not sure how long will it take me to clear custom & immigration. Arriving 12 noon. Would 1320 train ride be sufficient time to get to my train. What does Insieme means?

Just buy the train ticket when you get to Pisa Centrale. There are plenty of trains leaving from there to where you want to go. I went to Pisa on a daytrip from Monterosso two years ago in July and bought the return 15 minutes before the next train departed there was plenty of space. There is going to be a correspondence (meaning you will have to change trains) somewhere depending on the time you travel more than likely in the aforementioned La Spezia.

Thanks.
Should I also use Trenitalia for train service from Pisa Centrale to Milan Centrale?
There is another website I saw called Loco2rail booking. Is that another train company? Should I just stay with Trenitalia? How many kinds of train are available for me to use?

Loco2 is a middle man broker online booking service that sells tickets on Trenitalia the national rail line of Italy.
There is private own company called Italotrain also:
https://www.italotreno.it/en
Italo does not service Pisa.
Use Trenitalia for Pisa to Milano

oh yeah use whatever site that does not mark up the prices you see on Trenitalia.
People use sites like loco2 because they may find it more user friendly than Trenitalia e,g, you do not have to use the Italian language spellings when you search

bg,

A few comments to add to the others......

Where is your flight to Pisa originating from? You likely won't be dealing with "Customs" unless you have something to declare. If you're coming from outside the Schengen zone, you'll need to go through "Passport Control / Immigration" and have your Passport stamped.

As Laura mentioned, you'll first use the automated People Mover from Pisa Airport to Pisa Centrale. There's really no reason to buy tickets in advance for your trip from Pisa to Monterosso, as many of the trains on that route are Regionale so prices are always the same. Buy your tickets at Pisa Centrale, either from a staffed ticket window or a Kiosk. As previously mentioned, you must validate (time and date stamp) Regionale tickets prior to boarding the train or you'll risk hefty fines! There will likely be one change of trains at La Spezia Centrale, which is very easy.

If you wish to buy discounted tickets for express trains (Freccia, Intercity) for other parts of your trip, one of the easiest websites to use is www.trainline.eu, which sells tickets for the same prices as the rail networks. Registration on the site, including payment information, is required but once that's done the site is very user friendly.

For the journey from Pisa to Monterosso, there's absolutely no reason to look at Italo Treno as they don't operate on that route.