MostToysWins is correct
If you want to get a good sense of what bullets in general do to living things in general, spend time reading the hunting forum, especially regarding deer and larger animals. You will learn that even with "enough gun" and "enough bullet" there are enough other factors in
any given shot on any given day that there is just NO ANSWER to your question. This is because rifles are, by definition, more powerful and more accurate than most any handgun, and if THEY don't have an answer that will drop a deer everytime, then you can be SURE that there is no handgun or no handgun bullet that will somehow provide that.
This is just the way it is.
What YOU need is a gun that you are comfortable shooting, that you can control, that you can conceal, and that you can afford. That includes the ammunition, not just the gun. If you get a 9 mm, you will pay less for a box of 50 bullets than you will if you get a .40 or a .45. That means you can afford more practice, which affects your control and comfort. If you get a .22 you can REALLY afford bullets, but you won't get quite as much oomph per shot if you ever need it.
You have to get a chance to shoot different calibers and pick one you like and one that works out those first three issues above.
Good luck. You'll spend a lot more time shooting for fun and practice than you ever will defending yourself, so it will be good to pick something you'll enjoy for that too!
Springmom