@testpilot I've always assumed the minimum power was the 8 Ohm rating, since that's typically what's sold, but of course, if your speakers are 4 Ohms or less you also wan to make sure that amp has the current drive for it. Ideally find the minimum impedance, and/or the minimum effective impedance.
So if your speaker maker recommends 50 W minimum, but is 4 Ohms you'll want an amp that produces 100W or close to it at 4.