I'm not sure about the trilogy, but the first game was amazing, I loved it. And Infinite looks fun, but I was never really on-board with 2. Something about being the first Big Daddy didn't really work for me. That said though, I never got round to playing 2, so perhaps I can be swayed. Give it your best shot.
First game is amazing, this is true (one of my favourite games ever, actually). Second game isn't as good, but still decent and Infinite is kinda like a Call of Duty take on the series.
All of the games are a lot of fun, but it reminds me of the Mass Effect trilogy in terms of development throughout the series. With each game more focus is brought onto the combat, but to be fair to it Infinite's story was quite good, even though it felt more like a corridor shooter than a Bioshock game. In fact, I'd go as far to say it was the story that made me finish Infinite as I started to grow a little tired of the rinse-repeat gameplay - the 'Burial At Sea' DLC is quite interesting, I loved returning to Rapture and seeing it before it fell to ruin.