I wouldn't consider Birth by Sleep to be a side game as it is waaaaaay too important to even be one. Heck, it is the longest Kingdom Hearts game to date (on average, 45 hours of game-play). It has so many plot twists and plot tie-ups that neatly connect all the games together, and it sets up the major events for the upcoming Kingdom Hearts III. Basically, half of KH3's plot will be based on whatever happened over eleven years ago in Birth by Sleep.
Chain of Memories is nice, but not necessarily needed to play unless you wanted to fully understand the motivations of all the characters in Kingdom Hearts II. It helped me better understand Namine's and Roxas's relationship with each other. At first, it seemed superficial until I played Chain of Memories (because Namine states something about a promise, or something like that. Can't remember; it's been a while since I've played CoM).
358/2 Days is alright if you don't mind the repetitive game-play and slow movement of plot. The only important thing you need to know for Days is Roxas's intent for leaving the Organization, Axel and Saix's relationship with each other and the plot they hatched, Xigbar's sight of Ventus, and Xigbar's and Xemnas's hidden motivations.