My first memory of Batman is tied up in both the Super Friends cartoon and what has come to be called the Batman '66 television show.
But my first comic book? After some web searching, it was Batman #260 (a 100-page special).
I remember a story where the Joker has poisoned Batman who will die laughing. And things just keep getting worse as the Joker tells horrible punning jokes. The Joker is freeing inmates from Arkham, and Batman comes up against Two-Face who has a gun stolen from a guard. This was my first encounter with Two-Face as he wasn't used in the TV show. Two-Face flips his coin and it comes up heads, so he doesn't shoot Batman (who is on the floor laughing painfully), and allows Batman to lock him back up in his cell.
Looking at the cover, I can vaguely remember the story with the Riddler, but the rest are a blank to me.