Honestly, I'd play Bioshock 1 and 2, and then maybe give Infinite a shot.
Infinite wasn't bad, but I thought Bioshock 1 and 2 were way better. The art deco style was way more appealing than the "turn of the century America" look of Infinite, Infinite's choice to revert to the 2 gun system was a mistake, as well as the regenerating health system. I'm also a sucker for any games that involve the ocean. Likewise, I found the original's plots to be WAY better, especially the funky take on objectivism, free markets, communism, ideology, etc. Infinite was essentially just "racism is bad".