I have run a weekly game for eleven years and I have prepared for it well maybe a third of the time. What I do have is a five minute routine I run while people are joining, and it has saved more sessions than any amount of writing ahead ever did.
Open the scene you actually need
Not the one you ended on. If the party said they were going to the harbour, the harbour is the scene that should be up when they arrive. Loading the tavern they left and then switching in front of everyone is a small thing that quietly tells the table you were not expecting them.
Put one thing on the map that was not there last week
A cart, a fresh scorch mark, a person standing where nobody stood before. It does not need meaning. Half the time a player invents the meaning for you and it is better than what you would have written. This is the single highest return per second of prep I know of.
Decide what you will say yes to
Pick two things you are willing to let the party do that you have not planned for, and decide now that the answer is yes. Doing this in advance is what stops the reflexive no that comes out when you are surprised in the moment. You will not use both. You will be glad you had them.
Check the one number that matters
Whatever your system tracks between sessions, look at it before anyone can ask. Rations, supply, the countdown clock, the thing that changed while they travelled. A GM who has to look something up in the first ten minutes has already handed the pacing to the rules.
Everything else in your notes can wait until someone gives you a reason to open them.
