Like many others I'm sure, I downloaded Bioshock Infinite for free as part of the games with gold for March, and bought the first Bioshock for $5. (probably won't get the 2nd unless it's cheap and seems worth it).
Does it matter what order I play them in? Is there a way that will be more fun?
I heard the story is unrelated but I'd still like an experienced player's opinion.
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Bioshock Infinite has pretty much nothing to do with the first one, so you're fine. Play it in whichever order you want!