I recently finished BioShock Infinite, the last of the three main BioShock games. Previously, I had also played BioShock 1 and 2.
Here are the trailers for all of them.
1 and 2 are very similar and in the same world, whereas Infinite is completely different.
I liked everything about Infinite except the actual combat gameplay. There were great environments, story, music, characters. I’d call the actual combat gameplay “uninspired”. You didn’t have to work too hard compared to the previous games. So if you have to choose, I’d recommend 1 and 2 over Infinite. BioShock 2 is #12 on one list of best FPS-s. Infinite was in some sense more of a cinematic story where the actual gameplay and shooting was secondary.