I thought by the title of your post you were going to be 40 or 50 or something. Anyway, my mother knows a woman who started karate when they were 50, so I think you will be fine. However, some clubs seem to only have kids as beginners, and at 14 you might want to join an adults club or class if all the other beginners are 5 or 8 or something.
I started karate when I was eleven, did it for two years and began again when I was 16 (until I was 19, started again at 22). My brother is starting jujutsu at age 14, my mother is starting Japanese sword and naginata at 54, my partner started sword at 30, and many of the martial arts clubs around here are mainly populated by university students - jujutsu, eskrima, karate, kung fu, taekwondo, whatever, you name it.
To choose a club, I recommend going along to a few clubs and trying one or two classes. Maybe get a parent to watch too. And then ask yourself and your parent - what do you think of it?
Do they yell at you too much, do they seem safe, is the instructor just out to pump his own ego, do you think you would be comfortable there, are the classes disciplined, will you get out of it what you want, was it fun

? These questions apply to all martial arts and people of all ages.