Hi Dave,
It may sound silly but I feel like a bit of a cheat using auto. I went to Duxford last Sunday which is where I used the Nikon for the first time in years and although I'm really pleased with some of my photos, particularly the spitfire which was in motion, I don't feel as though they're 100% mine as I didn't really use any skill in taking them, if that makes sense. I know moving off auto will be difficult and will take a lot of practice to get non blurry photos but I think I may feel more of a sense of achievement with my photos for doing so. When I use my Panasonic I've started to turn auto off as feeling a bit more confident with it and my photos of horses jumping have started to come out non blurry which I'm really pleased with. I know I still have a long way to go but I would like to feel the same with my Nikon. As I say it's a silly reason really.
There has been a lot of 'discussion' in the thread about 'what is auto' that is probably not particularly helpful to you.
What it sounds like you are after is more influence over the final look of the photo - rather than purely deciding what is in or out of the frame (which is the one thing that even on auto a camera can't yet do - and is the basis for any photograph - your choice of subject).
Actually, you do make one more decision that influences the look of the image - your choice of focal length - use a wider angle lens and get closer, or a longer focal length and take the shot from further away - the relationship between objects in the scene will be different.
The next 'choice' you can make is the one you are thinking of - which is the balance of Aperture, Shutter Speed and ISO - the 'Exposure Triangle'.
I suspect that most photographers who choose to move off 'auto' will actually use either 'Aperture Priority' or 'Shutter Priority' modes most of the time.
These are semi-auto modes, where you select either the Aperture (to control Depth of Field) or Shutter Speed (to control Freezing / Blurring of motion), and let the camera then determine a 'balanced' exposure by metering the scene and selecting suitable values for the other two settings.
This works well most of the time, but the camera can be fooled by a scene that has a predominance of light or dark tones - which is where 'exposure compensation' comes in, and allows you to put in an adjustment to the 'balanced' value if needed - you can also use exposure compensation to deliberately over or under expose an image fro artistic effect.
'Manual' in this context is where you select both Aperture and Shutter speed (and ISO, though some cameras allow this to be in auto mode) - the most common situation where this is needed is when working with manually controlled flash / strobe lighting (such as in a studio). Here, the camera cannot calculate the required settings, as the light isn't there until you press the shutter, so you have to tell it what to use.
My suggestion would be to read up (or watch a few videos on) the effects of Aperture and Shutter speed, and the 'Exposure Triangle', then go and practice / play a bit in Aperture Priority and Shutter priority modes - see how taking the same shot with different settings changes the image.
Once you've used them a bit you can decide if they are right for you or not.