Although it is not a perfect concealed carry pistol, a .22 will be much more useful for your stated purposes. I don't think I know anyone that is a really good pistol (or rifle) shot that did not learn how to shoot by using a .22.
A .22 is much more appropriate for small game and target practice.
If you do decide to find a pistol primarily for CC, a compact 9mm is a good way to go.