+1 for what LES wrote.
Ask a bunch of gun guys and gals what gun they would recommend and you will get 50 different answers. If we knew what she intended to do with it and how she intended to carry, her experience level and so forth, then we could help you make a better informed decision on what to try. I personally can recommend the .380 ACP Ruger LCP, but it's lack of proper sights make it a belly gun at best. It is, however, a couple of hundred dollars cheaper than a Kahr P380, ($375 vs. $685 MSRP) but you are getting a Kahr, one of the premier gun maker's for that size of pistol. In .32 ACP I can recommend the Beretta Alleycat. It has a tip-up barrel for ease of loading and they can be had with an XS Sights big dot night sight set for less than $400 out the door.
The little belly guns in .32 and .380 are nice, but not what I would recommend for a first pistol, nor a primary CCW. There are very good options in the 9mm class that are not much bigger or more expensive. They do recoil more, but you are getting a much more powerful chambering in a pocket sized gun. I can recommend the Taurus Model 709 (my wife's pistol) and Beretta Nano from personal experience. I paid $375 for my Model 709 and saw the Nano for $440 in a shop over the weekend.
Don't overlook revolvers. The Smith & Wesson J frame has been around for decades and for good reason. It works and works well. While not as powerful as a 9mm, the .38 Special still whoops a .32 or .380 anyday for power. The Taurus Model 85 is another good "pocket gun". I own a S&W Model 042 and a Taurus Model 85 and can vouch for both, with the Model 85 being my favorite. Ruger revolvers are also great and built like tanks. The SP101 is the pick there.
Also don't get stuck on having to buy a new gun. Right now it is a buyer's market on used guns and there are alot out there. People are dumping them like crazy here in Indiana in anticipation of the gun bans that may or may not take place. I have been picking up excellent condition used guns, several of which were as NIB, for 1/2 to 2/3 the original cost. Single stack guns and revolvers are plentiful, because the guns that are selling are high caps.
As LES says, put as many different models in her hands as you can, and shoot as many as you can, then let her choose. I chose my wife's first handgun for her which did not work out well for her. Now she has a single stack 9mm she says is a perfect fit, which will translate into confidence in the gun and herself on the range and in a defensive situation.
Good luck and congrats on you finally getting to exercise your Second Ammendment rights!