Before you do anything, go to a range and get some instruction. If you can find one that rents handguns, try shooting a variety to find what suits you best. If that is not an option, find an instructor and learn the basics.
Now come the bullet points:
First off, buying a good handgun will pretty much take care of your budget. Even a good .22 target pistol can run over $300 without anything fancy.
Second, what is your main purpose? If it is plinking and target shooting, I suggest a .22 handgun. Great for learning and easy to handle.
Third, if self defense is your purpose, which is what I gather from your desire to get a conceal and carry, than you really need to get some experience with a variety of makes and calibers before you buy. Full size handguns are hard to fully conceal. Smaller conceal guns tend to be less accurate (but more than adequate for standard self-defense purposes) and usually have smaller magazines. I never suggest anything lighter than a .380 for self defense. Anything above that (.38, 38 special, 9mm, 10 mm, .40, .41, .45, etc.) is, at least, adequate.