The adverbs that you listed are not exactly equivalents, even if they can all be used as intensifiers, as you say.
Molto and estremamente, together with tanto, assai, oltremodo, sommamente, straordinariamente and quanto mai have more or less the same meaning, and form with the adjective the "superlativo assoluto".
They are the preferred way to give emphasis or force to the meaning of the adjective.
Proprio, veramente, and davvero, but also realmente have a different meaning, and you should use them to say that the adjective applies really, and not necessarily in great measure.
Addirittura has still another meaning, as perfino and nientemeno you should use it to stress the fact that the adjective is applicable even if it could be not credible.
I advice you to check the adverbs on a dictionary and compare their meanings to better understand their use.