word choice - "Should" in Japanese

The word "should" in English has these uses when not used as a question:

1. To express the expectation of the speaker (Probabilistic reasoning).
   
   
   
   • The train should arrive in 10 minutes.
   
   
   
   


2. To express a condition
   
   
   
   
   • Should it rain, the event will be cancelled.
   
   
   
   


3. To express obligation or the duty of ~.
   
   
   
   • I should go home.
   
   
   • You should study hard for the exam.
   
   
   
   


4. To indicate an ideal state perceived by the speaker.
   
   
   
   
   • Everyone should have equal rights.
   
   
   
   

From my understanding, I use ~はず for 1., ~ば(or other conditionals) for 2., and ~べき for 3. .

(Question) What can I use for 4.?

Answer

2 could also use 場合 to be a little more formal (雨の場合は...). 3 can also use ～もの as another option to ～べき (猛勉強するものだよ！).

4 lacks a little context. While most of the time it will be perceived as subjective (i.e., "(It's my opinion that) Everyone should have equal rights," it could also be objective in a few circumstances. For example, "A new law passed. Therefore, everyone should have equal rights (now)," or something similar. Each case would use something different, and I'm thinking ～べき again if it's subjective and ～はず if it's objective.

I'd also add a #5 to your list: subjective recommendation, for which you could use 〜たほうがいい (and, I believe, also 〜たらいい or 〜ばいい).

お前、風邪【≪かぜ≫】気味【ぎ・み】だね。今日学校を休んだほうがいい。　→　You seem sick. You should stay home from school today.