If you are looking for a plinker, I suggest that you get something similar to your primary handgun. So, if you purchase a Smith and Wesson Ladysmith in .38 special, consider a .22 lr revolver. You can plink with the later and you can apply the same muscle memory to both.
Regarding the Ladysmith, someone else here mentioned it and I think it is a good choice. As a man with medium sized hands, I find it comfortable to shoot. Yet, at the same time, it is designed for just the kind of carry (and gender) that you are describing. As an aside, if you choose to carry in your purse, consider getting a pocket holster or a purse designed to carry your firearm. This will help to keep lint and other debris out of your weapon and may help to keep the firearm oriented properly.
Someone else here mentioned the 1911. I am in awe of the 1911 and consider it to be, far and away, the finest handgun ever conceived (sorry to all who disagree, I am a happy bigot on this matter). It could be a good choice for the full size handgun. There are, however, a few reasons I would skip this design in your case. First, if you lack dexterity in your thumbs, operating the safety may be difficult. Second, if you follow the recommendation above for a .22 LR and a .38 Special revolver, the 1911 is a departure from an operational standpoint. Thus the owner will lose some of the training benefit of plinking.
Regarding training, NRA courses are a good start. However, firearms training can range from explaining which end the bullet comes out of to courses taught by retired Delta Force operatives. If I were you, I would start simple and then continue training as I thought was fitting to my personal needs. Less cryptically, this means taking an NRA course and, possibly, a concealed carry course in your state. Often, these are one and the same.
Finally, another post recommended going to a range that rents weapons and trying several out. This is excellent advice. I wish I had followed it myself when I was getting into firearms. It would have literally saved me thousands of dollars and heaps of disappointment. If your local range doesn’t offer this service, several do so keep looking until you find one.
Anyway, I am banging this out quickly. I hope that this post makes sense and that you are a law abiding citizen. Feel free to ask me for clarification if I have failed to explain something clearly here.
Good luck.
THank you. I will try to find such a range here in the hinterlands.