I think one of the significant factors for what Redleg pointed out could have to do with the theatrical aspects of many civilian martial arts. As people have mentioned styles, such as Krav Maga, kickboxing, and judo, which do involve less theatrical dynamics, you can take those as indications to consider a martial art that is more straightforward in nature, if you're determined to learn one that may seem practical for military standards.
Do some research on: Krav Maga, Kickboxing, Sambo, Wrestling, Boxing, Judo/Jujitsu, Aikido, Karate*, Muay Thai, Ninjutsu*...
*Karate, these days, has some sports elements in it that can be impractical for real life situations. You want to be aware that not all Karate instructors may be willing to digress from the standards of the ring. Otherwise, Karate does have a number of simple, straightforward techniques that could prove useful.
*Ninjutsu has received a lot controversy over the years, primarily for its controversial history. However, despite the babble, Ninjutsu generally implements a mixture of effective techniques from various martial arts styles. There can be theatrical elements in some areas of its teaching, but there are also many dirty techniques taught that are naturally very effective (e.g. eye-gouging, throat strikes, joint locks/breaks, chokes, etc.). Athough I included it in the list, it may be somewhat complicated getting hold of a reliable intructor... unless you travel to Japan.
I specifically pointed out Karate and Ninjutsu because they are the styles I am most familiar with, and therefore have a little more input on. They are not necessarily my recommendations.