IMHO it does not matter much. The original Bioshock does not figure into Bioshock Infinate until very late in the game..and then not in the game p roper but ine long "Interactive Movie" sequence that ends the game. And eventhen it's a brief scene.
But I STRONGLY recomment you play the original Bioshock (Or the remastered version) before you play the "Burial At Sea " DLCs for Bioshock Infinate. Although they use the BIoshock Infinate engine and one chapter takes place in COlumbia, it is really much more of a prequle to the first Bioshock then a sequel to Infinate. A lot of the Burial games will no tmake much sense unless you have played the original Bioshock. And that previously movie you get ot try to fill yo in is pretty much worthless.

Infinite is like a conclusion, I think it should be played last.
And yeah Burial at sea you really need to play to bioshock 1/2 before, just to see how was Rapture before the civil war after you played the destroyed one

I 100% agree you should play Bioshock One before p laying Burial At Sea; don't see the need for playing Bioshock 2. TBoishock 2 is fun, but really does not add much to the background of the BIioshock Universe.

You should play it in order.