Bioshock 1 is lots of fun. It has an amazing story and it handles well. It's a bit stiff compared to later games but still easy to pick up and go. The entire series has similar controls so besides a bit of remapping between games it's similar.
You can get B1 fairly cheap or get the two pack for under $20. 2 is a direct sequel to 1 where Infinite is... not. I found 2 to be the least of the three. I didn't find it was as well done as 1 in most aspects.
You don't have to play the first two as the story isn't really connecting to BI but sometimes there is references or information that you may not get if you haven't played them. Nothing that would ruin the story, just little things.
If you only want to get one, get Infinite. If you want to spend a bit more, get the two pack of the first two with it. Bioshock 1, even if you know the twist, is still a great ride. B2, kinda, but not so much. Infinites' story is crazy and amazing. I was blown away and I've played it multiple times. The DLC that just came out is a separate story (sort of, it's a loooooooooooooong story) but still jaw dropping.