Become useful , and come in handy are the only phrases I've heard, among the several you've listed.
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The usual North American idioms are "come in handy" and "turn out to be useful." "Come in useful," a perfectly correct British idiom that expresses the same thing, is immediately comprehensible though slightly off-sounding to many American and Canadian ears, although it has probably become more familiar even there, as it is frequently used by J.K Rowling.