Full suspension bikes are typically for REALLY rough offroad. Like mountain biking in the mountains. Front suspension is getting more popular on bike path bikes, but I think that's kind of a waste; they're usually pretty smooth.

Being a woman, you have one less thing to worry about with drop bars.; no frank 'n beans in the way down there. The only thing to consider is weight on your wrists and the kink in your neck from looking up. Can you cope with that for more efficiency? One other thing to think about is that the more weight is on your wrists, the less is on your butt & back. It's always a delicate balance. A good mix might be drop bars, but just not too low or far forward with relation to the seat. If you buy drop bars & decide you made a mistake, you can always go Mexican-style and turn them upside down for a nice upright ride!