First-person shooters are not my favorite genre. I played my share of Doom, Wolfenstein 3D, and Quake like every other nerdy high school and college student in the 1990s, but they always took second place to strategy and role-playing games. So it takes something more than just running around with a weapon and a target-rich environment to convince me to devote time to a shooter. BioShock is one of only two such series that have done that and held my attention enough to play all the way through. (The other is Mass Effect, though I've yet to try the new Andromeda entry in that series. Probably not a coincidence that both have science-fiction aspects.)
BioShock and BioShock 2 take place in the 1960s in Rapture, an underwater city with a steampunk feel that's populated largely by genetically modified monstrosities. The environment has a post-apocalyptic feel as you pick your way through what remains of the once-luxurious city. BioShock Infinite is a bit of a different animal, as it takes place in a floating city called Columbia in the early 1900s. Unlike Rapture, Columbia isn't a run-down wreck and many of the people are normal civilians. (At first, anyway. Plenty of destruction as the game progresses.)
In both games, you pursue leaders who created a dystopia while following their own vision of perfection. In Rapture that largely takes the form of genetic modification, with lots of physical and psychological manipulation to keep the resulting monstrosities under control. In Columbia, you're working against an elitist, racist cult. There's a "grand society gone wrong" feel to both Rapture and Columbia, paired with a mix of old and future technology. That combination reminds me of golden-age science fiction in many ways; playing through these games feels much like reading some of those old stories.
In Rapture, there's a major moral choice in whether to save or harvest "little sisters" that provide power for your genetic modifications. (Personally, I have a hard time believing that anyone doesn't want to save the little cuties.) The choices don't have a lot of effect on the gameplay, but the ending differs based on what you've decided to do along the way. Nothing in BioShock Infinite's Columbia setting seemed to provide the same kind of moral decision-making, which was a little disappointing.
The two settings do eventually connect, but not until near the very end of BioShock Infinite. There's an add-on story called Burial at Sea that was released as DLC for BioShock Infinite that makes the link much more explicit. I thought the add-on was very well done, worth playing for anyone that enjoyed BioShock Infinite, but it's clearly targeted for people who have played the games in both settings.
I played these games mostly to work my way through the story, so the actual gameplay mechanics weren't my main focus. I purposely chose the easiest difficulty mode to avoid getting stuck in long fights, and picked abilities that minimized the need for shooter skill. For instance, in BioShock 2, I picked up the Security Command ability and upgraded it so I could summon a robot to fight for me. You can't ever avoid the shooting entirely, but it can be made less painful. Even so, there were sections where I had trouble making it through alive. Fortunately, death is a temporary state in these games.
It's possible to find some replay value in the BioShock games, either finding different ways to fight or changing moral choices to get different endings. None of that appeals to me, though. Most of the fun for me is in discovering things about the world as I move through the story. Once those surprises are gone, it's no longer very interesting, even if there are some differences. And playing with more difficult combat, like BioShock Infinite's 1999 mode, holds zero appeal whatsoever for me.
The BioShock series is well worth playing through at least once for any gamer. Even if first-person shooters aren't your thing, the story and world-building are worth the effort.