<p>What is copyright licence type to select in order to make the code free for the public in all possible ways.</p>

<p>Is "The MIT License" the best option?</p>

Releasing your code as
public domain
is the best way to make it free for
all
possible ways.
SQLite
is a well-known public domain library (they have
a page
that explains their license).
Having said that, code that is in the public domain can be simply taken by anybody else and they can call it their own. This is why there exist free licenses like GPL/BSD/MIT/etc where you retain some semblance of ownership over the work.
Personally, I prefer licenses like BSD or MIT because they aren't as restrictive as the GPL. The GPL has a lot to say about what the user of the code can and can't do with it.