You could both be agent you a sniper DPS and she a Operative heal spec. Genrally DPS chars are the easist and most forgiving classes to learn first, being a tank or healer in group play means you have a bit more responsibility and as you level up more is expected of you in group play. That is not to say DPS dont have an important role in group play just that there is a bit more leeway for mistakes.
Personally, if you're playing with your wife, I would not recommend choosing the same class. It's just a lot of fun to share in the other person's class story. If you have the same exact class story ... no variety.
It seems this thread agrees, though: one of you play Powertech Tank, the other play Operative Healer. They work well together, get great early companions, and can share in one another's class storylines. If you play any FPs, you will be looked at to lead, but friendly folks will help you learn the FP if you've not done it before--just let them know up front.