What I think of when someone says a "singer's club" is a place that's open to the public so non members can chance or happen apon the club & sit in to listen in or join in if they wish or ignor or stay off from it in say the main room of a bar instead of being in a side or back room or on a different floor froom the singers. I also would expect to pay a small fee to be charged to enjoy the pleasure which would hep the club to stay afloat & to help pay for the once & awhile special guest singer that would get paid to perform during asinger nite but here the guest singer would to a larger amount of singing while the floor singers would still sing but the focus would still be on the guest. Being an American & living in a country where this type of venue is not at all common I'd leave it to the Europens to give you a better discription though. To me it sounds like you're starting up a sing around on singing session which I'm far more familar with.
Good luck what ecer way you do it

BTW you said you're in the South, south what or where?

Barry