As a healer/support, you'd probably be looking at either a smuggler or a consular. The smuggler can do good dps and one of their advanced classes can heal. (I've never played a smuggler, but I know for a fact that they're a ***** to kill in warzones). The consular again has 2 advanced classes, the sage or the shadow. For you I'd recommend the sage as they are a ranged dps/healer. I am playing the sith mirror class right now and it's a lot of fun.
For your girlfriend, she should consider either a Jedi knight , Jedi consular or trooper.. The Knight has 2 advanced classes, Guardian and Sentinel. The Guardian is primarily a tank, but can do moderate DPS if specced into the right skill tree. The consular again has two advanced classes - the sage is ranged dps or a healer and the shadow is a tank or DPS. If she rolled a trooper and wanted to tank she'd need to pick the vanguard advanced class.
So, in summary:
You - Look into either a smuggler or a consular
Girlfriend - Look at either a jedi knight, consular or trooper.
I'd recommend reading up about them online and deciding then. Having said all this, you have 12 character slots, so you can always just roll one of each, play them for a bit and decide which one is for you
Hope this helps, let me know if you have any more questions