The only option unlocked at the beginning (except for purchasing premium items) are the Light Side Battles.
After the intro to the game you'll find yourself with these two characters:
Jedi Consular
Clone Sergeant - Phase 1
These are two great characters who you'll probably be utilising for much of the whole Light Side Battles section.
All characters have special abilities. The Jedi Consular is what is known as a Healer and has the special ability to heal his whole team. The Clone Sergeant is more of a basic character, but his ability to target the whole enemy team with one shot makes hum continually useful as play through the initial stages of the game.
Let's go straight to the first battle. It should be pretty easy. Take note of the 'cooldowns' for each of you character's special abilities. Usually the weapon button to the left can be used with every turn, but the ones to the right usually have a cooldown of a number of turns before they can be used again.
The game does guide you through this initial battle.
Then guides you through the process to gain your third character:
Clone Wars Chewbacca
Chewie is what is known as a Tank (and a Scoundrel), he can taunt the enemy and force them all to attack just him for a couple of turns, his high hit points allow his to absorb a lot of punishment.