Hey, I really feel you on needing to get away from an abusive mother! It's awesome that you've come so far. Just one thing... if you're going to buy a gun to protect against her, you should be prepared for the possibility that you will use it on her. Do you want to go there? If not, mace, pepper spray or a taser might be a better investment. Something to incapacitate her if she tries to assault you, but not something that will have the potential to kill her.

You might also want to look into self-defense classes, and definitely figure out how to use the pepper spray/taser. Just fyi, if you are mostly afraid of an attack in your house, a taser is your best bet - the pepper spray would cloud up in your room and you would get a dose as well.

As for making her leave you alone, one time-honored method is to act as though you're even crazier than she is. Unfortunately, you can't really do this unless you're already in her presence. If she does show up, though, you can skip the remaining calm and reasonable stuff, since that doesn't seem like it works, and go straight for the arm-waving, yelling, throwing things, and generally acting like you've lost your mind and might do violence to her at any minute. This is sad to say about your mother, but you want her to be afraid of you.

Good luck and I'm sorry you are going through this!