Grats on your very first home-grown peppers.
Pics that show the flower, calyx and number of fruit per node would be helpful.
But just going by the one pic you posted, the leaf shape suggests some kind of annuum to me.
As for when to harvest, you will know it is ripe when the pod changes to its final color. Often that color will be red, but other colors are possible. It is fine to use chiles when they are still green (think grocery store Jalapenos) but they are usually at the peak of heat and flavor when fully ripe.