Anyway, you don't need to play either 1 or 2 for Infinite. If you didn't play 1 or 2, you will miss out on one small thing at the end of the game, which I can catch you up by saying "BioShock 1 is about an underwater city."
But I'd say just skip Infinite and buy 1 and 2 instead. 1 is the best from a total story perspective (world, characters, writing, etc), 2 is the best for gameplay. Infinite is a really mediocre game and the most overrated game of all time imo for a litany of reasons which basically result to "everything about it is bad EXCEPT for a the plotline, but all other aspects of the story (characters, world, etc), gameplay, etc suffer for a plot, so why the hell is it a game not a movie?"
One of these days, Valve will confirm Half-Life 3, but nobody will believe them and assume its another ruse.
You definitely gotta play 1 man, it has a reputation for a reason. Beautiful use of Art Deco, fantastic atmosphere, and it's a pretty lengthy game. Only problem with the combat is it can feel a bit clunky at times when the battlefield starts getting hectic (Peach Wilkins fight for reference) but with that, the game gives you opportunities for preparation and playing smart. Something you definitely don't get in Infinite.
If and when you do get it, just.....make sure to stay away from gamefaqs or anything that talks about its story.
I'ld also recommend playing Bioshock 1 at least once before Infinite. It's not needed to understand the story, but it is by far the best in the series. The problem is, after you play infinite and especially 2, the combat in 1 seems very dated. This is mainly because you can only wield a plasmid or a weapon at once. IE. if you have your shotgun out, you need to hit the plasmid trigger twice to fire a plasmid and vise versa.
As other stated, 2 has the best gameplay hands down. Bioshock is one of my favorite games of all time, I've beaten it 30+ times, but after 2 I find it hard to go back simply because the combat and stupid hacking game. (It's fun the first time through, but not when you're beaten the game repeatedly.) Bioshock 2 doesn't have a great story, but it has the best weapons and plasmids. Bioshock Infinite is still a great game, but definitely not a masterpiece like Bioshock. I'm hoping Burial at Sea will change my opinion though. I'm waiting on my return to Rapture.
I'm actually going backwards in the series. I just beat Bioshock: Infinite on 1999 mode, now that there's nothing really left to do (maybe find the last 10 missing voxophones I haven't found) I'm going to pick up Bioshock 1. Gotta prepare for B.A.S. so I kind of know what's going on!