If I could pick three classes for each side I would say these are the three classes i would do:
Republic: What would be cool here is an Republic Agent does special forces work plays similar to imperial agent, the next class i would do is Baran Do this is a force sensitive class they have different abilites they don't use a lightsaber and instead you a staff focus on martial arts fighting and force technics whirlwinds, lightning, force push ect.., the final republic class I would do is the security officer, So this class job is essential to be a officer of the law going after bounty hunters, criminals, spies ect.. I think I would have him play similar to the bounty hunter
Empire: First off the empire needs a trooper the exact same similarites with a Republic trooper, The next is the Pirate which is pretty much the same as the smuggler except i would let him have the ability to have a sword as well, and my final class is that of the Nightsister. Night sisters focus more on force powers they dont use lightsabers normally and use force powers making them a compliment to the Baran Do on the republic side