I think it depends on the variety and how green the peppers are.
Some peppers do fine from green to ripe but others need to be a little riper to be picked early.
In general,I like leaving stuff on the plant as long as I can before picking it.
Sugars,heat etc. develope better on the plant I think.

I agree with smoke. I wouldn't pick until I was ready to use it. If your worried about pod production, most plants can support multiple pods. An obvious exception would be if it's early in the season and the plant is too small.

Tim

+2
I agree. For most chilis, if I want truly ripe peppers, I wouldn't pick them until they are ripe on the plant or at least, starting to turn ripe. For instance, a Hot hungarian wax pepper will be a yellowish green color while growing. But once it starts to ripen, it will turn a shade of orange and shortly after will go to a nice bright red color. If you want "ripe" ones, pick them when red or at least orange going on red. That being said, many peppers are normally picked and eaten when still green such as a Jalapeno which will eventually turn red. There is a bit of taste and heat difference between them and it is a matter of personal preference. I generally pick and process most of my Hot Hungarian wax when they are still yellowish green. I do this for a few reasons.
1. The flavor and heat suits me fine at that stage.
2. I usually don't want to wait too long. Any time after they reach mature size, I will pick them.
3. It allows the plant to get busy and put it's energy into producing additional pods.
Bruce

Welcome to the pepper community! I suggest experimenting, some peps are much better when picked in unripened state such as the Aji Crystal.

I published an article on this topic a while ago, I will ink to it below.

Here is a link that might be useful: Pick'em!