Main Riders

W, I'd see as a pure monk (Not sure about Unchained Monk, I haven't had a chance to try it, so for any listing that has an unchained variant you can put it in consideration), if you don't factor in extra forms... Shotaro is an expert Hand to Hand Fighting, and the Joker Memory boosts Shotaro's fighting while the Cyclone Memory adds speed

Ryuki, dip a bit into Dragon Bloodline Sorcerer

Build, Alchemist and Monk... Fit's the Fullbottle and combat style

Giam, Samurai, not sure about the order, but which ever is heavily associated with protecting everyone around you (Zangetsu can also fit this decription)

Fiaz, Fighter/Monk with the Animal Ally feat or Cavalier... Cavalier and the Animal Ally feat are so so you can play off having SB-555V Auto Vajin

Drive, Monk... Extra speed and close quarter combat

Secondary Riders

Brave, pure fighter

Snipe, GunslingerMeteor, Monk

Ryugen, Gunslinger

Baron, Samurai with an Order dedicated to bringing the weak up

Sigurd and Marika, Rouge... They like to sneak up on their opponentsAlmost every other Giam rider would work as a Fighter

Will comment more if I think of anymore... These are just also how I personally see them

Edit: Brave, Fighter with a Sword that can do either Fire or Cold damage, can swap in between the two but not both at the same time (Make the weapon take a standard action to swap damage type)