So, my thoughts are, above all else, hit what you intend to hit. Once you can do that, push the pace until you can't do it and then back off and work on the accuracy again.
Great posts by Dan Chamberlain, RJM & others.
I've always strived for what Dan is saying above, probably because the 1st type of competitive shooting I did was BE, where accuracy is what counts, but it's carried over into all other types as well.
I also believe that good & on-going physical fitness certainly elevates ones quickness & also helps with the mental attitude & focus no matter the endeavor.
Probably the 2 single lessons that I've retained forever from my competitive shooting is front sight focus & trigger control.
Once trigger control is mastered, all else is more or less automatic........get the gun up, on target & then muscle memory from learning & repetitiveness simply takes over & the gun goes off, almost of it's own volition.
Doesn't really matter much whether it's a pistol or a rifle, hunting or competition.......or something else. (Assuming that you do intend to shoot, in the 1st place)
Training & practice simply continue to reinforce what (hopefully) one has already learned.
I do think there are 3 distinct types of shooters though:
Those that are naturals & need minimal training
Those that are not naturals but can become good shooters through training
Those that will never be good shooters no matter how much training they get.
YMMV
MM
