Use will for a future event you state as certain: I will call you tomorrow. Use should for advice or expectation: You should call her; the train should arrive by six.
Quick test: predicting something as settled takes will; naming the best thing to do takes should; saying what you expect, without guaranteeing it, takes should too.
When you are sure versus when you are expecting
You are sure about a future event, so state it plainly: The meeting will start at nine. Will fits because you are presenting it as settled, not advising anyone.
You are reassuring a friend waiting for a delivery, so you write It should be there by noon. Should fits because you are saying what you expect, not what you can guarantee.
You are responding to a colleague who missed a deadline, so you write You should email the client today. Here you are naming the best thing to do, which is exactly what should does.
You are promising a friend you will help them move, so you write I will be there at ten. A promise states the future as settled, so will is the natural choice.
You are writing to a guest about arrival times, so you write Your train should arrive at six. You expect it, but you are not guaranteeing the schedule; only a guaranteed timetable lets you write will in your own words.
You are guessing at someone's answer, so you write They should accept the offer. That shows you think it is likely but not certain. If you knew it for sure, the settled-future rule would give you They will accept it. instead. The first sentence reports probability; the second reports certainty. That contrast is the whole test: ask whether your sentence is settled, best-to-do, or merely expected, and the modal follows. It sounds stiff to write They will accept the offer when all you have is a hunch, and it sounds oddly hesitant to write should about a signed contract. Match the modal to how sure you actually are, not to how sure you wish you were. If you cannot decide, read the sentence without the modal: They accept the offer tomorrow works only as settled fact, so will it is. This mirrors the page's opening test but now covers all three conditions, including expectation, *
When should shows up with if
Try it first: finish this formal email, If you ___ need anything further, I will be happy to help. Pick should or will. If you picked should, that is right; the if-clause marks the event as a mere possibility, and will waits for the main clause.
You are writing a formal email about something that may not happen, so you write If you should need anything further, I will be happy to help. Here should inside the if-clause gently marks the event as a possibility, and will stays in the main clause.
The same sentence sounds stiff in casual speech. Talking to a friend, you would probably say If you need anything, I will help, dropping should and keeping will where it belongs. Treat should in if-clauses as a formal-register option, not a required one.
Now apply the full test to your own sentence. Settled future, like The meeting will start at nine, takes will. Naming the best thing to do, like You should email the client today, takes should. What you expect without guaranteeing, like It should be there by noon, also takes should.
One more case: a formal hypothetical clause. If your sentence begins with if and you want a formal tone, put should in the if-clause and will in the main clause, as in the email above. Informal tone drops should instead.