If your standard clothing attire doesn’t really support carrying concealed, think about getting a conceal carry purse. Mine has a zipper compartment accessible from the side of the purse, which can be locked, and has a holster built in to keep the gun secure.
Carrying on your person is more secure, but I would rather have a gun in my purse than no gun.
I like little snubbies.
One can fit in the coat pocket in winter (where it are immediately and discreetly accessible -- nobody thinks it odd that someone walks with her hands in her pockets in cold weather, and the fastest draw is to already have it in your hand).
You can find cargo-pocket shorts that allow you to totally conceal one in summer.
You can also use an inside-the waistband holster that totally conceals it when you just drape a t-shirt or vest over it.
As others have noted, the best gun is the one you're likely to routinely have with you. Just train yourself into the habit of continuing to fire until the bad guy goes down.