Should I tell everything about the cause of depression to my first doc. Visit.?

It's about trust. The first visit to a doctor is the meeting of two strangers, so the establishment of trust is most important. Ideally, you would want to feel comfortable sharing everything with your doctor. Only you can decide if the doctor has earned your trust enough to do that. It's helpful to let the doctor know there are things that are difficult to talk about and see how he or she reacts.
Absolutely yes. The only way for a physician to help a patient to the best of his/her ability is to know all the details of a particular problem. Many patients either downplay the truth, bend it, or outright lie for a variety reasons that seem legitimate to the patient. Ie- embarrassment or distrust are commonly used as reasons. We as physicians want to help- therefore need the most accurate description.