Every martial art has something to offer. Not all martial arts are best for self defense. The question must be asked though, what is self defense? To truly be able to defend oneself a variety of skills must be harnessed, as well as certain ones must be avoided. There are disciplines and forms of training, while both brutal and effective, will get you killed. Any school of art that is focused on competition should be avoided. Sports have rules, regulations and referees, things you will never encounter at the end of a knife gun or in a street fight. So if you walk into a Brazilian Ju-Jitsu school that focuses heavily on MMA training, you might not be getting the best training for self-defense.
3 Arts and Disciplines to start with:
Krav Maga: Created for the Israeli army you will learn to fight in close range, attack first, use any means necessary, and defend against weapons and multiple attackers. If I had to recommend only 1 art I would be this one.
Muay Thai: You will not learn how to strike any better in any other art. You can become competent in the art quickly. Since it is a striking it will work well with your flight or fight response. This would be the second art I'd recommend after Krav Maga.
Ju-Jitsu: this was my art for a long time so I am partial. The great thing about it is that is versatile and adaptable. Learn as many forms as you can. Japanese stand up for throws and standing locks, Brazilian for ground fighting and take downs, Danzen ryu for small joint manipulation and standing body mechanics.
The following are other arts I think hold important tools in self defense:
Aikido: This is an excellent art to learn avoidance, body physics and defense again rushing attacks.
Ninjitsu: To learn the psychology of fighting and strategy.
Kung-fu: the great thing about Jung-fu is that there are so many styles you will be able to find one that fits you and your body type.
Jeet Kun do: I think of this truly more of a philosophy then an art. Take what works, leave what doesn't.
Escrima: The ability to know how to use a weapon is very important and there is no better or easily found weapon then a stick. If you look around you at any given moment there is something to use as a weapon, chances are it will be long and cylindrical.
These are all arts that I feel have an important piece of the puzzle in terms of self defense. I eventually want to train, at some length, in all of them. If I had to give a top 3 to learn immediately it would be 1) Krav Maga, 2) muay Thai 3) Ju-jitsu.