Introduction
The write-ups in this node are great, but I thought I would add my input which presents different focus and organization. I write this to target those people who are seriously interested in practicing the martial arts but have no significant previous experience. Furthermore, this document is intended to guide someone in selecting an art, not a school. As you are likely aware, there is such a thing as a crappy school that teaches a great art. While some issues require some overlapping between art choice and school choice, I will try to avoid it when possible.
Research, Research, Research
It is simply dumbfounding how different some martial arts are from each other. This makes it very important to do a lot of research on the different arts so that you can make a good decision. If you end up choosing at art that doesn't fit you, it's likely you'll give up and never try again. But if you find something you love, it can completely change your life.
This article outlines many things you should know about each art you look at. I can't provide lists of arts, their ideas, their concepts, et cetera because that's simply not feasible.
I think that it's also important for the potential martial artist to know that most martial artists try more than one art. Even if it sounds perfect, you may try it out and find that it doesn't quite fit your taste. No big deal, just renew your research and try something new!
Availability
Obviously, you are going to need to choose an art that you can be trained in near your location. You may do your research and say, "Eskrima is definitely the art I want to practice!" but then much to your dismay, you discover there is no place to learn it within 500 miles.
Location may also help you practice more often. It's a lot easier to make up excuses for missing a class when you have to drive an hour to get there.
Physical Limitations
If you have a bad knee from an old football injury, then I wouldn't suggest something with a lot of low stances and focused footwork like capoeira. It should be pretty easy to determine which arts to rule out because of your own physical limitations as long as you learn about the styles (see below).
Safety
Some arts are more prone to causing injury than others. A huge consideration here is that of sparring. Do you want to regularly fight other students? If so, what rules are you comfortable with? Also keep in mind that the more physically intensive arts are generally more conducive to injury. Most other safety considerations are school-specific as opposed to art-specific, so I won't go over that here.
Current Body / Desired Body
What kind of body do you have? Know that many martial arts were developed in locales where race was mostly homogenous and diet was limited. This is especially true in many Japanese arts. What this means is that the art was developed by and for specific body types. As such, you may want to throw this into consideration, although honestly, it isn't much of a factor these days.
What kind of body do you want? Do you want to be large and powerful, or lean and limber? While you can always do your own body conditioning outside of the school, know that many arts are likely to build your body in a specific way.
Practicality
This is a highly argued topic, so I'll try to present this in a noncontroversial manner.
The one binding attribute of all martial arts is that they have some focus on fighting. As such, I believe that if you study any art hard enough and long enough, you will have skills applicable to real world situations.
However, I cannot deny the fact that some arts have more focus on taking techniques to the street than other arts. So really the question here is "how soon do I want to be able to fight effectively on the street?" Most arts these days provide some quick and easy self-defense techniques early in training, but after that things vary greatly.
This is another category that relies highly on what you want out of the martial arts. If real world application isn't something you desire, that is completely acceptable.
Weapons
Do you want to learn weapons? What kind of weapons? Do you want to learn modern weapons, or weapons from ancient China? Would you like to focus on swordsmanship? Or stick fighting? How about archery?
Find your answer to those questions, and then research the different arts to find what they focus on in relation to weaponry.
Style
What do you want your martial art to look like? Do you want it to be fast and fierce, or slow and graceful? Maybe you desire no aesthetic appeal whatsoever. Find high-ranking people who study whatever particular art and watch them -- see if that's what you want to look like once you reach that level.
Formality
Different styles range in formality from "very traditional" to "don't give a fuck". Some people won't be comfortable in a formal situation whereas others demand it. The best way to determine how formal an art will be is to look at its lineage, or better yet, watch a class.
Lineage
It is important to research the lineage of whatever art you may be considering. The most important reason for this is determining its credibility. Many arts will claim that their lineage is some 2,000 years old but when you actually read about its history, things seem sketchy at best.
Another important reason to look at lineage is so that you can get an idea of the conditions in which it was created and for what purpose. Was it developed in prisons to avoid getting shanked? Which part of which country was it developed, and what was going on there at the time? What kind of body type did the practitioners of that art have? What kind of diet were they on?
Also know that just because it's a "traditional" Chinese/Japanese/wherever martial art, doesn't mean that it's old. Aikido, Taekwondo, and many styles of karate aren't even close to being 100 years old. So, if you're looking something that's been in development for at least 100 years, look elsewhere.
These things can tell you a lot about the art and whether or not it will fit your desires and needs.
Spirituality
Some people seem to be under the impression that the martial arts will make you "one with yourself" or "one with the universe". This is a difficult subject, so I will tread lightly . . .
One difficulty about this subject is defining what is meant by "spirituality". You might think of it as having to do with the supernatural, or you may regard it as a word to describe our internal emotions and thought patterns. As such, I'll try to be really generic about this. Let's do this in a negative/positive format:
Mastering a martial art won't make you Buddha. Yes, there are fighting arts that will have you do various meditative exercises. But remember that these are fighting arts. Meditative practices in such cases exist to improve your fighting skills. That's a shortsighted statement, but it's important to not get ahead of yourself. What binds all martial arts is that they center around martial conflict resolution. Even if you're doing Tai Chi Chuan, which seems nice and calm, the fact remains that its real world application involves violence. You are directly or indirectly (depending on the martial art) spending a lot of brain focus on violence. It doesn't seem very conducive to enlightenment when you think about it. However, read the next mini-section and see the paradox . . .
Following the martial way is nearly guaranteed to enrich your spirit. Note how I carefully worded that last sentence. I didn't say "doing martial arts" or "learning self-defense". If you allow it to, the martial way will help you learn focus and discipline if nothing else. These are essential to a strong spirit. So in this regard, the martial arts may indeed help you find some sort of spiritual goal. But also keep in mind that it's all up to you. After all, you can find spiritual epiphanies in a bowel movement if you really want to. It all has to do with your perspective and willingness to commit.
Cost
Actual monetary cost is really more school-related than it is art-related, but I felt it was necessary to include. A lot of people don't think about the money it may cost and they often don't think about the time it will cost them.
If you don't have the time to train in the martial arts, then you won't be able to reach proficiency as quickly as you'd like. You can either wait until you have more free time in your life, or better yet, you could make some free time.