First of all work out just what you want from your martial art and compare this with what its practitioners and coaches say it offers you. Then watch a couple of training sessions and make up your own mind as to what it offers.
Do you just want to get fit, lose a bit of weight? There are many more effective ways. Do you want to meet new people -again, other clubs are more sociable. You used the word "combat", which should be a given in any martial art, but implies that you want to learn an effective fighting system.
Why do you want to learn to kick and punch? Is it because you have inner insecurities? Join the club! Have you been the victim of assault or violence? Why do you think a sport based on practising hitting other people will benefit you?
It has been observed often that martial arts practitioners (I do consider myself one)are more physically confident and less likely to be bullied or put upon. I have had personal experience of this myself. However ask yourself what your friends, family and others will perceive in you -is it a new, threatening, violent person? Will others trust you? Will they respect you or simply fear you? Is this what you in fact want to achieve?
Most people who take up martial arts are teenage boys, looking for respect, quite happy with the idea that other people fear them slightly because they are involved in a sport which many perceive as violent.
Ask yourself if you would be happy hitting someone in a heated exchange. You could end up being sued for very expensive dental work not to mention medical bills and a criminal record.
Why have you limited yourself to these four arts when you don't even know if you can practice them locally? What classes are there at your local sports and recreation centres? There are directories for most mainstream martial arts on the internet. In a few seconds I located a center in Hoover, Alabama. (See link) Likewise the yellow pages state directory has 151 listings.
Remember that most martial arts come in many different styles, some of which are so far apart as to be different arts altogether. Even Karate, which is widely practised, has a bewildering array, some of which are downright weird. There are instructors who will tell you how tough they are but train wearing jewelery and garish coloured silk pyjamas. Others will wear a simple, rough old cotton suit, say nothing but be able to project force with breathtaking speed and power.
Have you considered Tai-Chi, Yoga, Kendo, Judo (which is not classed as a martial art) or even athletics? Try running a 100m sprint against your local club champion and see who kicks ***! Try competitive cross country running and see how fit you get.
If you want a "unique" martial art, by definition, there will be very few practitioners! White Crane Kung Fu may not be widely available in Alabama. Then again, there are probably tens of thousands of Muay Thai practitioners worldwide (and another hundred thousand crippled ex-fighters begging in Thailand!)
If you really want an informed insight into martial arts I can recommend without reservation Rob Redmond's excellent 24 fighting chickens website, particulary the archives on karate philosphy and "Karate 101". He's American by the way!
Finally, in my opinion, if you were to pit fighters against each other in the four styles you mention:
Ju-Jitsu is primarily a grappling style so would only be effective if they closed with another fighter. I have no idea whether a Brazilian style of a Japanese art would be superior/more effective. Depending on the style of karate and whether a good practitioner, I would expect the karateka to beat them.
Ultimately, Muay Thai possesses the combination of professional, highly athletic fighters, devastating techniques and strength and stamina training which would be expected to see off any other style in the world, in my humble opinion. These guys play for keeps, cos there's a lot of money and status involved. Think pro-basketball but you are allowed to elbow and knee the guy in the head!