TL;DR You should be able to use ～はず or ～べき to indicate an ideal state perceived by the speaker, but a phrase that contains 理想 would help to emphasize that fact.
1. To express the expectation of the speaker (Probabilistic reasoning)
You say that you would use はず in this case, but given your sample sentence that sounds a bit too strong (unless you are really trying to emphasize the point). I think that ～だろう／～でしょう or even ～よう would be perfectly acceptable and probably more common.
"The train should arrive in 10 minutes."
電車はあと十分で来るでしょう。 (when you are expressing your belief or opinion)
電車はあと十分で来るようです。 (after looking at a timetable)
2. To express a condition
I agree with you in saying that ～ば (or some other conditional) would be appropriate in this case.
"Should it rain, the event will be cancelled."
3. To express obligation or the duty of ~
You say that you would use ～べき in this case, but the following would also work just as well.
In fact, I think that these are used more often than ～べき.
"I should go home."
"You should study hard for the exam."
Note that you can also use こと to express obligations (I often see this in bulleted lists).
"You should study every day."
4. To indicate an ideal state perceived by the speaker
Here I think that you could use either ～はず or ～べき, but to make it clear that you're talking about an ideal state it would probably help to start your sentence with a phrase containing 理想.
"Everyone should have equal rights."