If its strictly for target shooting, get a .22 LR, like a ruger mark III. The gun is cheap, ammo will be cheap, and the gun will be good for learning the fundamentals on. Women wont have any difficulty shooting it either.
If the gun is also going to double as a self defense tool, then get something in 9mm. Go to a gun store that has a good selection, and see what fits your hand well. How the gun feels, how the trigger pull feels(one of the most important things for shooting accurately), and how much you are looking to spend would dictate which exact gun is for you. Be wary of really cheap guns, like HI point, they arent going to be durable, accurate, or reliable.
A beretta 92fs is a reliable, accurate and safe gun. (although grip might be too large for women). They can be found for under 600 I think. Its also the handgun the US military uses, which is where I learned to shoot it.
Im not a big fan of concealed carry permits myself. Having a gun with you turns any confrontation into a potentially deadly one. Think of how many violent confrontations you faced as a paramedic, and how you survived them all, then consider how it would have went if the person assaulting or threatening you had grabbed a gun you were carrying, and how that would have ended. Or if you had drawn on them first, what if they dont back away, you gonna shoot em? That opens up a whole other can of legal worms.
Thats my take on it.