This is a question that I am often asked and I have noticed that many of my students have been feeling a sort of pressure to be shooting in Manual mode.
First let's understand why you would shoot in Manual versus another mode like Aperture priority.
In Aperture priority you set the ISO, the aperture(or f-stop) and the camera based on that information and the available light will choose the shutter speed. If you don't like the shutter speed you can either change the ISO or aperture to modify the shutter speed. Additionally you can use your exposure compensation (EV +/-) to tweak the exposure. When you use exposure compensation in the Aperture priority mode the thing that is modified is the shutter speed.
I start all of my new photography students in the Aperture priority mode because it is my feeling that this gives you a "safety net" because if you are not looking at your meter inside the camera constantly to make sure the exposure is correct. Also until you are familiar with the dials in 'Manual mode' you could be turning the dial the wrong way. This adds to the frustration of the new photographer.
In Manual mode you are responsible for the ISO, Aperture and Shutter speeds settings based on looking at the meter inside the viewfinder. The advantage of shooting in "Manual mode' is that when you are needing exposure compensation you can choose to do it either by adjusting your aperture OR shutter speed on the fly. The need for using the EV +/- now becomes unnecessary and also the risk of inadvertently having it set is no longer there.
So what is the best mode for you? The Aperture priority mode gives you a little more speed if you are shooting quick moving subjects or are in lighting conditions that keep changing.
Use Manual mode if you feel comfortable with it but not because you feel pressured to be a "real" photographer.
If you have a camera in your hand as far as I am concerned you ARE a "real" photographer!!