During the steam sale you could get all 3 for less than 1 of them.

Bioshock 1 is my favourite, my friends too.
However a lot of people have fallen for infinites huge size and great visuals.
Having played all of them I think they get progressively worse.
1 had a fantastic plot, addictive gameplay, great audio and a beautifull progression.
2 the plot felt forced, and the changes made didnt add much to the experience.
3 (infinite) was visually stunning but until the end it felt like an entirely different game, and at no point did I get fully immersed in it.
I think theirs an even split between supporters of 1 and 3, but on that deadlock basis id advise you to go for the first, and cheapest, bioshock game.
Iv never replayed a game as many times as I have that.

Simple purchase guide for Bioshock trilogy. Bioshock Infinite has the richest story ,character development and
without question,the best graphics and art design and thé most usefull sidekick ever , Bioshock. One remains thé most frightening, Bioshock 2 is thé weakest as it is à dialed in cash grab

BioShock is a survival game, pure and simple. Each enemy represents a threat, and it's best to sneak around enemies then smack them. It is easily the most immersive of the 3, and is really well paced.

BioShock 2 is a great game, but not as good as the first. The atmosphere is different and less charming, and you can tell someone else made this one. That said, it's worth a play, as it's still a very solid game.

BioShock Infinite... oh how I weep for thee. Columbia is beautiful and an amazing place, but that doesn't help the rest of the game. At tines, it feels like the relationship between Booker and Elizabeth is forced, but otherwise it's generally well paced. Later in the game, the story tries too hard to be deep and philosophical, but it's thrown in your face. The game is just like "lol 2deep4u." On top of that, all semblance of survival and exploration is gone. You don't have large areas filled gear you want, and combat is forced. The game proceeds at a pace of gunfight - Elizabeth and Booker chat - gunfight.

So yeah. Get BioShocks 1 and 2, and rent Infinite

Pro tip: Also try to get System Shock 2. It is only 10 dollars on GOG.com, and it has awesome extras.

I've only played Infinite, but I beat it and it was a fantastic game and I want to get my hands on the original BioShock sometime. I don't think you could go wrong with either, though. Maybe buy the first one right now because Infinite just game out last year and its price will hopefully drop eventually.