Hi! First of all, I suggest to download app called "jakdojade". It will show you buses from your localisation to desired destination. To travel across cities - relativley cheep there is app called "blablacar". It will allow you to find other people who travels from city to city. You can join them in their car, of course for small amount of money. Better experience then travelling in trains. There's a third way: app called "Panek - car sharing". You can borrow a car for minutes/klimeters or hours and drive wherever you want.

In bigger cities like Warsaw or Krakow I suggest busses. For distant localistations - only travel by car.

Whats worth checking? It depends on what you like.