I'm not impartial
I like Coheed and Cambria, and their music makes more sense with the Amory Wars. The music is better, but that's expected. This is the first four chapters in this collection, but there are two prior series that happen before Good Apollo and are pretty important. Start with Second Stage Turbine Blade, then read In Keeping Secrets of Silent Earth:3, and maybe Year of the Black Rainbow (Its not in graphic format). Or listen to the album's of the same name, there are quotes ripped from the songs out into the books; trying to put together a puzzle is fun without all the answers.
Is the story cheesy? No doubt. It starts pretty shaky and much cheesier, but it got noticeably better each collection... And maybe that same cheesy feeling holds a place in my heart. If that isn't your thing, you might be able to skip STTB and get enough background from IKSSE:3 to read this, but it won't be the same ride.