GOA to CT train or bus?

GOA - I had to look it up. Assuming you don't mean the place in India, I think you mean Genoa airport.

Long distance buses are not a thing in Italy, trains are a lot faster, a lot more comfortable and nearly as cheap; and you cannot get into the centre of any of the Cinque Terre towns by road.

1) Genoa airport to centre of Genoa. I am not familiar with this. It is a relatively short distance and a taxi may be the best option.

2) Genoa to Monterosso - train. Not complicated, easy.
Go to the Trenitalia (Italian Railways) website: https://www.trenitalia.com/en.html
Enter, from: Genova Piazza Principe (the main station), to:Monterosso, and your desired date and time. Then click on [Search].
It shows you all the times, there are regular trains, more than one every hour.
Most are regional trains, there is no discount for advance purchase, and it only costs € 9.50

I haven't done this one personally but will take a stab at it and cheerfully welcome corrections if anyone has them.

Looks to me like you take a Flybus from the airport to Genova Sestri Ponente Aeroporto railway station:

https://www.airport.genova.it/en/transportation-airport/

From there, take a train to Monterosso. Inputing the departure/arrival stations into a random Sept. Thursday (12th), I see all sorts of trains from 14:09 (probably too early) every 1/2 hour or so that you can take, and tickets are cheap. Almost all involve at least one change along the way. You do not need to purchase tickets in advance, and I wouldn't recommend it in case of a delayed or cancelled flight.

Use the Trentialia website:
https://www.trenitalia.com/en.html

Choose "Genova Sestri Ponente Aeroporto" in the "From" dropdown
Choose "Monterosso" in the "To" dropdown
Choose a date and approx. time; it'll show you all the trains from that time through the rest of the day.

(Editing to add: Chris, we were typing/posting at the same time. Not sure if there's a benefit to departing from one station versus the other? What are your thoughts on that? Or anyone else?)

Thank you both so much! Exactly the info I needed. I love this forum! (Again, crickets over on TripAdvisor)

Actually, if you can help, how do I get from Pisa Centrale Train Station to Pisa Airport (to pick up Hertz rental car). This is the next phase of the itinerary. TIA!

There's a People Mover that gets you from the Pisa train station to the Pisa airport in about 5 minutes. It runs several times per hour and costs 5 euro per person. Google it for more details.

Rach, airport websites can be really helpful, and most all of the bigger ones in Italy have English versions. Here's the website for Pisa's (which I have been to although not to fly to/from) and their page on getting to/from Centrale via PisaMover:

https://www.pisa-airport.com/en/the-passengers/transport/people-mover.html

Info on the Pisamover:
http://pisa-mover.com/en/where-we-are/

Taxi is also an option; the distance between airport and train station is not all that far.

Thanks so much!

Rach, that ticket from Genoa to Monterosso will very likely be for regionale trains, which means no seat assignments and that you MUST validate your ticket before boarding the train. Don't forget 'cause fines for unstamped tickets can be doggone unpleasant, OK?

Yes, thank you Kathy! - Rachel