The Galactic Republic....
Jedi Knight - Human
Jedi Consular - Miraluka/Twi'lek
Trooper - Cyborg/Human/Rattataki
Smuggler - Human
The Sith Empire....
Sith Warrior - Cyborg/Sith Pureblood/Human
Sith Inquisitor - Zabrak/Twi'lek/Rattataki
Bounty Hunter - Human/Rattataki
Imperial Agent - Chiss/Human
These are all IMO....i fell like these are the best fits for each class