About "standardizing on which negator you are going to use. Not or !."...

...that depends on the intent of expression evaluation. Word operators (not, and, or) bind rather loosely than otherwise (!, &&, ||). Just consider the output of the following...

perl -e 'print join(" ", (!0 && 0) , (!0 and 0) , (not 0 && 0) , (not 
+0 and 0))'
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It is ill advised to ask a beginner to standardise on a negator, as you put it, without mentioning the operator precedence level.