Gun enthusiasts encouraged to ping.
I suggest a quality .22 revolver. A hit with a .22 is better, it has been said, tham a loud miss with a .45
You have two design choices. Revolvers also known as wheel guns or a semi-automatic pistol. Revolvers are very foolproof especially for the new gun owner. They have a double action trigger which is a little slower but can be safer in less experienced hands.
A semi-auto means you have to rack the slide with your other hand to put the first bullet in the chamber. The alternative is having a bullet in the chamber and the safety on. Any defensive encounter will be very high stress and racking the slide is one extra step when seconds count.
In a revolver you could go with something smaller like a .32 or .38 caliber. Something like a Ruger SP101 .38 is a reliable and not expensive. Ruger has one in .32 which is less powerful but easier to handle. Even a smaller .22 pointed at a vital spot is deadly.
What you should do is find a reputable gun store and see if they have a CCW class. CCW is concelaed carry which means you could get a license to carry a gun, depending on your state. At least 32 states allow it. A CCW class costs about $50 but you learn all about gun safety and how to use a gun plus the laws on what you can do to defend yourself.
Consider joining the NRA or go to their web site and see what local resoruces they have near your home. The NRA people are awesome. There may be a NRA club for females locally or you may be able to find a woman in your area who can help you. I think a woman gun owner and even instructor can give you her experience better than a man If you can find a range with a gun store they can usually let you try out demo models.
I first learned about Sarah Palin in the NRA magazine about women gun owners during the Clinton admin. I think I remarked - wow she is pretty.
An attorney in my office building was a former prosecutor, gun owner and conservative. I think he carries but he said in most cases he would use Bear Spray.
http://www.google.com/search?hl=en&q=bear+spray+defense&aq=f&oq=
http://www.sportsmansguide.com/net/cb/cb.aspx?a=210581&kwtid=221822
http://www.stun-ningsales.com/SelfDefense/index.htm#Pepper
http://www.stun-ningsales.com/SelfDefense/wildfire.htm
It supposedly has 18% of something - pepper spray or something. He keeps a can in his truck between the size of a hairspray can and a small fire extingquisher. You can get a smaller purse size. I think the ones with more a pistol grip sprayer are better.
Maybe other folks here have better suggestions.
Lots of good info on this thread for you. As mentioned upthread - THE MOST IMPORTANT POINT - is to go to a gun shop that has a range and rent/shoot different sizes, actions, models until you find the right fit. It may even take more than one trip.
Buy from a shop; try to deal with the owner, if he turns you over to someone else in the shop that person will probably be well qualified. Avoid the “sports shops”, they may or may not specialize in handguns and probably will not have the best prices.
If you buy an automatic shoot it quite a bit when you first acquire it to assure its newness doesn’t cause it to jam - most don’t but some may be factory-tight and require “breaking in”. It could require 500 rounds before it becomes jam-free. Which is another reason to start with a revolver.
And then shoot a lot. Handgun proficiency is a perishable skill.