This is a thread worth re-booting...for range firing...my experience:
Most of us right handed shooters began low and left...I say "right on track" and completely normal.
Safe dry firing is something I highly recommend. "So why is it when I dry fire I can keep the front site level and hit the imaginary bulls-eye??"
Answer: you are completely relaxed and
know the weapon will not fire.
There's nothing natural about something exploding in our hands.
Point#1)
For me, until I realized the grip, front sight orientation, and trigger pull need to all work together my shooting was spotty at best. My first shot at the range was almost always on target as I was simply following the good practices used during dry fire. Once that first "explosion" happened I began tightening up hence hammering the trigger because now I
needed to know when the gun was going to fire. Call it anxiety or whatever you want.
Point#2)
For me, until I realized that my support hand was actually used
for support, I still had problems. What works for me is 60-70% of the energy to grip the weapon for recoil comes from my support hand allowing my trigger hand to be relaxed. Under these conditions, you can really concentrate on that smooth, slow trigger pull without jerking the gun downward when firing. Does it take practice? Hell yes. You really do not want to know when the gun will fire under these conditions; you must convince yourself "why should I care when the gun fires, my support hand is in control".
Last Point)

For me, once the above mentioned points were in place, I could really concentrate on the front sight orientation making that the most important part of my shooting. At that point I could stay completely focused on keeping the sights on target until the weapon magically fired. The thought process at that point is truely keeping the sights on target for as long as you can controlling "wobble" until BANG!