I'm gonna be totally honest: I've never really sat down and listened to any Fall Out Boy. I've always just passed over them or I was exploring some other band. Where do you die hards think I should start?
Honestly, after only knowing maybe four songs from TTTYG and FUCT, I pretty much started out with Infinity on High, because someone gave it to me as a gift when it came out in 07. I was hooked. Then I went back and listened to the older 2 albums. Then I got Folie when it came out.
So maybe just start with infinity on high. That way, when you go back and listen to TTTYG and FUCT, you'll see how they progresse. Then Folie a Deux.