I suppose it really is up to personal preference.
I however was taught to do one step at a time, you know, prep first, tips/forms, base layer, etc... On all ten fingers. The instructor told us that would make it quicker, but I don´t know if that really is true.
I guess as a beginner it is easier to do one thing at a time on all ten, so you remember each step and it is surely performed on all fingers. (In my case for example, when I did my left hand first and then my right, I forgot the base coat from my right hand.. whoopsie.. :green
And also I would think if you do one finger at a time, it does take more time, because it means opening and closing a dozen of different product containers 9 times more. (Yeah OK its just about seconds, but still). Just a thought.
-- Edit: And YES I know those annoying fidget types who keep on leaning on their hands or playing with their phones. Not a cool thing when there´s inhibition layers on which should stay untouched! So that was a cool piece of advise to never let go of the hand I´m working on (or in my case as I do both, never let go of either of them! So it might be a good idea to do one hand at a time for those clients...)