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One idea is a set of powered speakers, and a small behringer 802 mixer to front them.






That thought hadn't even crossed my mind, but it's worth looking at. I already have a Behringer XENYX mixer (not rack, but paid for)

How much of a signal do powered speakers need?

My preferred option is to find a singer who already owns a PA system...




Your XENYX will have enough output - they just need line-level inputs. Be careful of JBL powered PA speakers - I've had two different occasions where there were cold solders inside the case (fortunately the cases could be opened and I had a soldering iron with me).