The modern version of "it is as well" is "might as well". Or "may as well", with the difference in nuance between may and might.
E.g. "Although it may be two years before the world changes, change it certainly will and
it is as well to be ready for it."
Same as: "Although it may be two years before the world changes, change it certainly will and
it might as well to be ready for it."
As for the two example sentences with "should" and "had better", check out these two pages:
Had Better | ENGLISH PAGE
Should | ENGLISH PAGE
To me, "had better" is a lot stronger than "should", for "should" is merely a suggestion (but that can change with tone). "Had better" has more of a sense of urgency and warning that something unfavorable will happen if you do not listen.