Which is the best med for mood stabilization, least side affects?

There's no "one size fits all" answer to that, especially with medications designed to improve mood. That's extremely individualized. Even psychiatrists don't know the answer to that in advance. But they know the drugs. So they'll be in a position to know what might be some good candidates to try. But everyone is different and reacts differently. One antidepressant will be great for one person's depression and not do a thing for another's. You need to be guided by your doctor's advice on this question.