Hi Japan,
I don't think there is any need to avoid
had better, any more than you should avoid
can
for requests. Both can be considered abrupt if they are not
uttered to familiars or in appropriate situations. For first
person, of course, it is fine.
I need to go suggests an external necessity, where
should and
had better suggest a stricture of some sort; nevertheless, they are often essentially synonymous in use.
I had better finish my post now.