You have received excellent advise so far. I would add that, even though a .22lr would not be my choice for a CCW gun, they are excellent guns for learning tools for trigger control, and sight picture. They have low recoil, muzzle blast, they are cheap to shoot, which means that you can practice cheaply. There are many lightweight and reliable .22 pistols out there, made by the major manufacturers.
For a carry gun, you might try a .357 Magnum. A carry gun will be carried a lot, and shot little. You can practice with cheaper, light .38 Specials and save the Magnum loads for serious social work. If you train well, you may not even hear the boom when you shoot to save your life.
Once you have chosen a gun, you need to choose a holster and belt. It is of great importance that you choose a good quality belt that is stiff enough to support the weight of the gun and/or extra magazine, light,etc... The holster needs to cover the trigger guard completely and still give you a proper firing grip on your gun. Do not cheap out on your belt and holster. You can expect to spend $150 for a good set, more if you want fancy ones.
A problem that you have is that men are comfortable wearing clothes that are very alike, and generally, don't pay much attention to what other men are wearing. On the other hand, men are generally, acutely aware of women, and their appearance. This makes carrying a concealed firearm a bit more difficult for women than men. Women are mostly seen with a purse, so men generally ignore them, unfortunately thieves also know that they are a bag for valuables. Try to avoid the temptation to carry off body. If you are carrying a gun it is important to make sure it remains under your control at all times.
Belt holsters tend to jab women in the ribs because women generally are shorter between the waist line and the lower ribs than men. There are a number of quality manufacturers of civilian versions of belts made for police women, such as Galco, Bianchi, Safariland. The same for belts. I prefer belts from Looper Leather, in Oklahoma City.
If you wear business suits to work, Men's Wearhouse is very gun friendly and offers alterations for CCW. They do reinforcement of waistbands, extra protective patches on the inside of pants, jackets, etc. These keep the gun from eating a hole in your clothes. You can wear your gun into the store for measurement, no problem.
Finally, there are a number of manufacturers of very specialized female gear for CCW. Congratulations to those ladies who have taken responsibility for your own safety, and the safety of your loved ones. Welcome to the club!