Streets of Rage is the beat 'em up I have played the most. It was practically my introduction to the genre, and it set a high bar. It had intelligent enemies, three vastly different characters, a relatively nuanced combat system, and spectacular boss design. It made pretty much every competitor look like they weren't trying, even SEGA's own Golden Axe. There was just no comparison: Streets of Rage had won out the early-genre shuffle.
We're going to be playing as Adam, my personal favorite of the three protagonists. He's completely missing from the second and third games, as well, so this works out just fine.