Coloring your hair can be damaging if you lighten it. I go way more into it in my book, but for now, when you lighten your hair, you use peroxides, which hurt the protein that makes up your hair. If you use temporary colors, or even semi-permanent colors, that should be okay because those don't use any peroxides, or very mild ones at the most. If you color your hair darker, that also shouldn't do too much damage. It's that to lighten your hair, you need to use a really strong peroxide, and the lighter you go, the stronger the peroxide needed to do the job, so the more it eats away at your hair. An alternative might be to have highlights. That way you only damage a tiny percentage of your hair instead of all of it, but you still get some lighter color (if you want it lighter).

Now, if you are planning on keeping your hair short, it isn't that important anymore. You can color it all you want, because you'll be cutting off the damage anyway. If you want to grow your hair, then it's best to keep the damage to a minimum and stick with mild procedures, or just highlights.