I'll second that a good focus to start is setup and back swing. The last time I played with Mike (mvmac, one of the site owners), he made the comment that most people can play in the single digits with only two of the the keys in their 5 key system: steady head and weight forward at impact. I agree that a good starting place for you is figuring out the elements of steady head through the back swing and initiation of the down swing.
Note that steady means in all directions. You 100% can't have movement along the target line (towards your front or back foot) or forwards/backwards (towards your toes or heels as you stand over the ball). Some guys can get away with some up/down movement (towards/away from the ground) without movement in the other two directions, but building the swing from the ground up I'd recommend against that as well.
For me, there are two major requirements to a steady head on the back swing. First, don't let your back hip drift away from the ball down the target line on the back swing. For me, at the range, I have to actively feel the weight on inside edge of my rear foot. Second is not standing up. This is usually referred to as maintaining your spine angle, which I like as a swing thought but isn't quite anatomically correct. One good drill for this is the butt against the wall drill, which you can find on this site or on google. You can also just take very slow practice swings and concentrate on not moving your head at all to try to get what that feels like.
One note on something that's thrown me off for years. With a solid back swing and a less flat shoulder turn, I feel like I'm taking a much shorter back swing, and you may in fact do so. That's okay! I often subconsciously try to make up for it by rolling my wrists around or bending my front elbow at the top. Those both cause big problems, at least for me!