Seashell, there are some important variations on the dip.
If you lean forward a lot then you will activate the outer, upper pec very near the delt. If you keep your torso as perpindicular as possible then you'll isolate the triceps more.
As for depth, you need to lower yourself until your upper arms are parallel to the floor. That's deep enough.
The dips I'm talking about are for chest, but I can't really SEE if my arms are parallel or not... I'm going to ask someone to watch me do one set and tell me.
Seashell, I just go whatever my range of motion at the given angle is (while still maintaining form). My chest dips are shallower than my tricep dips if that helps.