Self defense against an attacker is a skill that most security guards should acquire. A self-confident demeanor is a must when confronting drunk, obnoxious , aggressive or violent people. Knowing that you can successfully defend yourself will give you confidence and erase any look of fear that would help empower your opponent. Remember, you must be the Alpha, the one in charge, the one that everyone respects because of the confidence you exude. In some states a self-defense course is required as part of a guard's training.
Boxing is an excellent way to defend yourself, but the martial arts provide a more "calibrated" response to violence. It is easy to hurt someone a lot, but difficult to hurt them only a little. And you aren't being hired to beat up on people. Skills involving leverages, pressure points, and takedowns are preferable when removing a rowdy patron or subduing a violent individual. Training in the use of weapons such as the baton or staff will allow you to defend against a more formidable opponent.
In the author's (biased) opinion, the best system for self-defense is Kung-Fu San Soo. Schools are located throughout Southern California and in some other parts of the country. San Soo is basically a street-fighting technique that teaches punching, kicking, leverages, pressure points, takedowns, and weapons.
One more note: UNLESS THE JOB REQUIRES IT, DO NOT CARRY WEAPONS. You are only asking for trouble for yourself and your employer If you injure someone there is a good chance you will be prosecuted (regardless of the circumstances) and your employer will be sued. If you have that much fear, you do not belong in this business. Also remember that any weapon you bring can be taken away and used against you. As the old street saying goes, "never take anything into a fight you don't want shoved [down your throat]."