I recommend reading the grammar points themselves because they go a lot more in depths about the nuances. But here’s a short list for some of the ones you’re struggling with. I’m leaving out anything with but/however because a lot of it has to do with politeness levels, but I also don’t fully know the nuanced differences between some of them.
のほうがいい - it’d be best to
ことだ - こと means ‘thing’ and when at the end of a sentence it can mean “it is a thing that …” implying a “command” to do something. Therefore, it typically is used in relation to “rules” and implies a sense of authority.
はず - assumption of how something should be; expectation (ex: 今桜はここにいるはずだ - It is expected that Sakura is here). Another note, はず is a noun. So we can get stuff like そんなはずはない - Such an expectation does not exist
ベキ - should in the sense of moral responsibility - you have a responsibility to do something; you ought to do it
なくて… vs なければ…
ないと - Similar to above, but now using と conditional (implying that if something is not done, then the following result will happen (more emphasis so to speak than ば, so more urgency implying something must be done)
…いけない vs …ならない - from what I’ve learned, this is the main difference between the two:
いけない - subjective, feels like you need to do it
ならない - you were told to do something, or people are expecting you to do something based rules or beliefs you follow
Hopefully that helps. And if anyone sees something incorrect/slightly feel free to correct me.