I took the train from the Gdansk airport into the city - it is dirt cheap, but there is one wrinkle - even if you buy a ticket to Gdansk Glowny, the majority of trains stop at the station before, so you have to move to a different platform and get on the next train. There is an information desk in the airport after baggage claim - you could ask there for clarification.
I saw many Bolt cabs in Gdansk, Warsaw and Krakow - Freenow as well - you may find that you will have to wait to create an account in the Bolt app until you arrive in Poland - although you can download before leaving home.
Warsaw is built on a very large scale, and while public transportation is excellent, you may find a cab useful in the evening.
Jakdojade is quite helpful in Poland as a trip planner for local transportation - you can also purchases in the app, but I believe you need to load a cash balance first. And there are different validation requirements for some cities - I believe that in Warsaw you need to shoot the QR code above the vehicle door upon entry, while in Krakow you need to enter the tram car number. You may find that buying a paper multi-day pass is easier for Warsaw and Krakow - it may not be worth it in Gdansk, which is amazingly compact. And perhaps you'll receive passes as part of the tour.
I arranged for a cab to the airport through my hotel in Krakow - it turned out to be a black car service - at a way too early hour - I was amazed how busy the airport was at 5:00 AM. Cab took 20 minutes at that time.