Now, there are several people far wiser and far more badass than me who have a bit to say on the topic, but I suspect that I reach a different demographic. I also intend to address studying martial arts for the purpose of improving oneself as a choreographer and/or performer. I'll also address self defense training a bit and how it might differ from what you might usually think of in martial arts.
Before I go much further, I'd say the first law in picking any physical discipline has already been laid down by Rory Miller: "Train in something that makes it a joy to move."
That being said...
Whatever your politics, I would also suggest taking a basic course in firearms safety. If your image of how firearms work is rooted in their portrayal in popular entertainment, a basic safety course can be incredibly enlightening. These are often very short as well.
With that out of the way, here are some basic tips:
First, explore your options in terms of geographic accessibility. If you cannot get to class, it does not matter how good the class is. You can take a long trip for a seminar or special training, but if you have to travel an undue amount of time each time you train, you will end up not training as much. An extension of this is cost. If you cannot afford the dues, you will not continue either.
Where you live will determine what is available. If you are a college student, you probably have access to numerous clubs. Take a look at any that sound interesting. Don't try to do too many at once. If you're in a major city, chances are you have a lot of choices too. Look beyond storefront schools (though do not ignore them as options by any means), many really great clubs do not have their own spaces.
Teacher is far more important than style. In the end you are not so much picking a martial art as you are picking a school/teacher. At one point in my masters program at NYU I went to my advisor to ask about what courses I should take in the following semester. I came to him with a list of topics. He put it aside and said to me, "Chaps, not maps." He told me it was not as important what I was studying as who I was studying with. I was in a department populated by all manner of pioneers in the field. A great teacher will illuminate any subject, and can pass on an understanding of the larger field trough any facet of it. Conversely, studying a subject you love with a horrible teacher is never a good idea. I had the good fortune of studying with an amazing sensei early on in my training. That set the standard for me in what a teacher should be.
I have often told people to never study martial arts with a teacher who was not funny. I do not know why, but all of the best martial arts instructors I have ever met have been hilarious.
Some sort of pedigree is often a good sign but they are no guarantee and the different means used to establish them can be misleading.
Avoid what are known as "McDojos." Nothing good comes of them.
Anyone telling you that they will teach you the grand ultimate unbeatable system is not worth your time. If the school looks like it might be a cult, that would also be a reason to avoid it.
I would also urge you to include boxing, fencing, and other practices in your search. We tend to use the term "martial arts" to only mean Asian practices, but combatative training is universal.
Watch some classes/take a sample class. If the people are performing activities that you want to jump up and take part in, that's a good sign. It does not matter if the style is unarmed, armed, or both. You are evaluating whether or not the movement system you see being practiced is something you would enjoy doing and if those skills are things you want in your muscle memory.
Expect to suck at first. But remember that sucking is a temporary condition in the learning of a new skill set. Martial arts have slow learning curves on the whole. Don't attempt to demonstrate anything if you're asked "Show me what you learned today." That said, stick to it for a while and see what you think as you get better. Some forms have far steeper learning curves than others, but you might feel that certain skills are worth waiting for.
Once you have some options, think about what you're looking to get out of the practice. Self defense? I covered that earlier. Beyond that, I want to go back to Rory Miller's statement of "Train in something that makes it a joy to move." You might be just as happy or happier in a ballet studio (and many of the same rules would apply). Fitness? Cultural experience? Rampant bloodlust? Community? Look at the people you'd be crossing swords with/rolling around on the mat with/hitting with sticks/etc. Are these people you want to spend time with? I've met many of the people closest to me in those contexts. I've also observed classes and schools where I've wanted nothing to do with the people.
Notice that I've said nothing about any tradition being better or worse than any other. This is in part because that is a bullshit line of thinking, and in part because (as I said before) it depends what you're looking for and who is teaching it. Do the thing you think you'll enjoy. If you don't enjoy it, do something else. Take a good self defense class regardless.
Are you looking into martial arts for adding to your choreographic palette? Which (considering most of the people who read my blog), brings me to...
Things to consider if you're taking up a martial art for the purposes of expanding your abilities as a choreographer and/or performer:
The martial arts were not made for stage portrayal. Aesthetically pleasing movement is a byproduct, not a goal. Some of the most effective techniques are too subtle to be effectively used in storytelling. Please do not confuse or conflate martial arts training with stage combat training. Their basic goals are in direct opposition. Martial arts can do wonders for your stage combat practice, but they are not the same.
Staging martial arts is more about what the audience thinks martial arts look like than what they actually look like.
You have two directions that make sense to go in: what systems would increase your ability in what you already know, and what systems would take you out of your comfort zone and push you to learn to think and move in new ways. A grappling system will help you in very different ways than a striking system or a sword system. Each has definite benefits.
If you're a choreographer, you might learn some moves you want to figure out how to simulate on stage and then move on. Nothing wrong with that. Just be sure you stuck around long enough to get a good working understanding of the context of the system you are working in. It's a good idea to explore.
A self-defense course is still a good idea beyond the obvious benefits as it will help you compose and contextualize pre-assaultive behavior in your fight scenes.
Take a gun safety course. Regardless of your political views. Because you will be working on scenes with firearms. And you should know how they work.
For the record, I compiled a resource page of martial arts info for stage combat types a while back.
I spent most of my life practicing various martial arts and combat sports and have also done a fair amount of teaching. They occupy a major portion of my scholarly work and a significant portion of my artistic work. I'll say again that there are far wiser and more badass people out there than me, but there has not been enough said about how to begin training or pick schools.