You must be American lol! The train is a much better idea. The train station is actually in the airport near the passenger terminal. You'll get into the city centre a lot quicker and it won't be expensive. It'll be much cheaper than a cab.
I would say the train if during the day. Very convenient I heard. Uber was about 100 zl if I remember. That was in October and not to the city centre, a bit closer to the airport
the link to the timetable doesn't work (in english the Polish version works but only to march 12 at present).
I'd take the train over a cab. I might take the bus but with luggage it could be awkward (and thieves sometimes specially target airport buses so you need to have Polish situational awareness... which you probably don't have).
If you do take a cab make sure it's reputable (some airports will order you one, which won't be the cheapest but won't skin you alive either....)