Winamp seems fine to me. Plays the stuff I want playing, and seems reasonably intuitive to use.
I don't know if I'll try this gizmo though yet awhile - I get a bit scared by advice like "Don't forget to shutoff original WinAmp CD plugin by changing its extension, for example 'in_cdda.dll.off'" on that download site...
But thanks a lot NancyZ, because it might be very useful indeed, and I'd never have found it otherwise.