I almost exclusively run PBTA games nowadays because of this. And if the players are totally inexperienced we'll run a one-pager like Lasers and Feelings or Honey Heist first.
Rules just bog down the play speed too much unless everyone is an expert, paying attention, AND not drunk, which is basically never.
I used to print out spell sheets and put them into some sort of a spell booklet for reasons like this. It also helps that I played a bard when I did that and so there wasn't a whole lot of spells that I needed to keep track of.
The last time I played a wizard, I just relied on a similar tactic (one-spell sheets compiled into some sort of a booklet), but instead of printing it out, they just stayed as files that I move to a directory on my phone called "prepared spells".
I had a pretty disastrous fight with my wizard, so I came up with a little list of "when X happens, use A,B, or C". That made combat much easier, since it had a list of escape methods for when I was cornered, spells to deal with invisible monsters, stuff to deal damage when I was in a safe spot, etc.
It only had five or six entries, but it made my turns way faster in combat.