For most directories you do not need a separate membership plugin. What to use depends on what you want to charge for.

Charging businesses to be listed

Use the GeoDirectory Pricing Manager with GetPaid. You create packages for each post type and choose the price, how long a listing stays live, whether it renews, and which fields and features each package includes. Users pick a package when they add a listing and pay through GetPaid. Start with the Pricing Manager setup guide. To sell several listings in one purchase, see how to sell package bundles.

Charging people for a site membership

For user accounts, registration, login and profiles, use UsersWP. It works with GeoDirectory, and its Membership add-on adds paid membership plans. See the UsersWP Membership setup guide.