Which method of checking if a variable has been initialized is better/correct? (Assuming the variable could hold anything (string, int, object, function, etc.))
It depends if you just care that the variable has been defined or if you want it to have a meaningful value.
Checking if the type is undefined will check if the variable has been defined yet.
=== null or !== null will only check if the value of the variable is exactly null.
== null or != null will check if the value is undefined or null.
if(value) will check if the variable is undefined, null, 0, or an empty string.