I'm personally not into Fall Out Boy (I mean I listen to their stuff but I'm not a crazy fan), but a good place to start is always what is popular. You may find that you like other songs better in the long run but if you got to start someplace, usually popular songs are easiest to go off of. Then you can start exploring more after that and before you know it, you'll be a well versed in Fall Out Boy repertoire haha!
I like their old music, actually.... I really like the song, "I'm Like A Lawyer With the Way I'm Always Trying to Get You Off (Me and You)" ... I don't listen to their new stuff :/