Which Bioshock should i play first?

1-2-infinite

Well, the first would be a good start. Because it's the first of the three I guess.

Play them in order, its worth it.

1 is by far the best, start there

1-2 and infinite ;D

Definitely the first one. I can't vouch for 2 since I skipped it, but Infinite is awesome, completed it on Xbox then bought it with DLC on Steam but guess what? Haven't got time to play it yet, lol

Hum Mullins recommendation sounds reasonable.
I try to come up with something different

Infinite - 1 - Infinite(Burial at Sea 1/2) - 2

You would need the season pass for infinite to play burial at sea.

what is the connection between those three bioshock?

The first one. Only the first one.

1 2 Infinite, 1 is considered the best by most I guess but IMO has the worst combat of the 3 because of the controls and if you play it after the other 2 you will see how badly the first one's combat has aged.

First Bioshock, then Infinite, then the Infinite DLC "Burial at Sea" episodes 1 & 2.

Bioshock 2 isn't that great. If you don't have a lot of other games to play then slip it in, otherwise safe to ignore.

I have played the whole franchise, I liked them in this order 1 - infinite - 2, however I strongly suggest you to play them in the right order, to do it properly...

So, would you kindly take my advice and start with Bioshock 1?

Bioshock 2 is great too, it's only just "more of the same", when compared to Bioshock 1. I loved Bioshock 1, for me it's still a benchmark as for what a virtual world created in a game must be and immersion. It's one of my favourite of all time. Since Bioshock 2 is more of the same, it really didn't bored me, I was perfectly happy about it. I'm not always looking for "something new" or "innovation" in a game. Sometimes it's just not necessary.
I recommend you play in release order: Bioshock 1, Bioshock 2 and then Infinite, just like I would recommend you too watch the first trilogy of Star Wars and only then the prequel trilogy. Same principle.

BioShock infinite was yuck

I'm one of those people who can't help but play games in order :-)

I started on the second cause the first's got no archievments lol
So I did 2-inf, cant say I regreet :)

The first one is, IMO, is one of the best games ever made.

Just so you know, bioshock 2 and Infinite's DLCs are worth playing. I just finished the series last week and it is really great to play them in order :)

i've still not gotten around to playing 1 and 2 or the DLC for infinite but it's on my to do list Marves den looks pretty epic for 2 ...you get to be a big daddy

If you care for plot:

Bioshock 1 before Bioshock 2, otherwise much of the plot of 2 will be lost. (Including the parts where contradicting philosophies still end up with pretty much same end-result.)

Infinite main game is independent from those 2 except for one scene tying everything into the same multiverse, so can be played whenever.

And the DLCS too. Don't forget about the DLCs!