I think it is best not to be impolite.
Is the above sentence fine, or should it have
better instead of
best in it?
Your sentence is correct. In Oxford English Dictionary one of the meanings of BEST is "most appropriate, advantageous, or well advised". Compare your sentence with the following: it's best if we both go.
That sentence is correct. I don't see much difference between that and
I think it is not to be impolite.
It is not either/or because both essentially have the same meaning, though the use of best is a little stronger than better.