Polished sets minimise noise but they are expensive and best thought of as icing on the cake - studio strings just to help that extra 5%. John Williams records with them, for example.
Coated strings will help you a little also, but the primary solution for this, for dealing with the quiet bass movements you mention in the subject line, is a technique issue and not a string brand issue. The solution depends on whether you are getting shift squeaks (fretting hand) or plucking hand squeaks, or both.
PS if you are playing plugged in the pickup will accentuate the squeaks.
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Jon
"The way nature seems to work is that it sends a messenger...the acoustic guitar needed to go in another direction, Michael Hedges became that messenger"
Tommy Emmanuel
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