Street Battler - Unarmed techniques, toughness, weak ninjitsu. [Streets of Rage / Street Fighter]
Shinobi - speed, stealth, swords, strong ninjtsu. [Dragon Ninja / Last Ninja / Goeman / Shinobi]
Engineer - intelligence, technology, academic knowledge. Building [Wily/Robotnik] / some brawling buyable [Zen: Streets of Rage 3].
Commando - Guns, strength, more guns; mowing down waves of enemies or sneaking/platforming around. [CONTRA / Bionic Commando]
Handyman - Street knowledge, investigation, toughness, unarmed attacks; jack-of-all trades, high utility, tough as nails. [Mario]
Dream Touched - Dream Land / Fantasy Zone / Chaos / Giygas / Other Realm magic. High chance of exploding or going insane. [Earthbound?]
Player owned Dream touched artefacts? (eg; God Hand, Vampire Killer)
Anti-Dream 'alien' artefacts? (Vampire Killer? Depending on origin story.)
Alien relics - Zora, Hylia, Chozo, mythrid of shooter enemy races.
Buyable cybernetics, buyable bioaugs. Possibility of playing as a bioroid (eg; like Sparkster / Sonic)?