I am 14 and want to start martial arts(Tak Wando probably) because I have heard it helps improve basketball as well. What age is to late to start? Am I "over the hill"?

Any age is fine to start martial arts.

The important thing is to find a school or instructor whom you can learn from.
They must be able to give you obtainable:
A. times for instruction.
B. close enough location.
C. affordable cost.
D. safe learning environment.
E. and reasonable expectations about progress.

Only if can find a place where you can trust, and be rewarded with respect back, should you train there. It is your choice, so choose wisely, but you are not locked into any one style, and can change what martial art(s) you study, or just study additional martial arts over time. Sometimes teachers move away or schools close, so also practice your basketball at the same time, to improve your basketball, but yes martial arts should help you with speed,etc.

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.

It's never to late to start.

As to what dojo to choose, do your research check them all out. Observe a few classes at each school.

Well I have to admit I have never had anyone 14 ask if they are over the hill, makes me feel older already.

But no, anytime is good, even those ancient 30 year olds can still learn some.

But again it is not an overnight improvement and you should want to learn martial arts because you want to learn it, if you merely want to get better at basketball just practice basketball more.

Many of the things you learn, self confidence, mind/motor skills will all help many parts of your life including sports performance. But only study if you want to learn the martial arts not merely to get a side effect.