I would suggest a Browning Buckmark or a Ruger Mk. I, II, or III. They are reliable, far more accurate, and to be honest, you are not endangering your safety by shooting these guns as long as you follow the four rules.
I suggest this route because Jennings' pistols are generally considered to be the lowest quality handguns one can buy, regardless of price.
My advice: Buy a good .22 pistol to gain some skills and get some good trigger time. Once you feel comfortable with it, buy something else in a sufficient self-defense caliber if you are interested in concealed carry.
Anything .38 Special and up for revolvers, and 9mm and up for autoloaders. Once you are confident with this gun and know how they operate internally and externally, concealed carry is a great idea after the proper training and certification.
If you just want something for plinking, a .22 rifle is my choice. A Jennings that may (or may not) jam all the time is not fun and not safe. A good .22 pistol is quite a lot of fun, a decent .22 rifle, when you can hit absolutely anything you want within 50-100 yards is TONS of fun.