Help please. I'm finishing my basement and have some questions re flooring choices. I've read here that too many different flooring products are a design no-no. Does this apply to basements? Basement is walkout and all flooring will sit on 1.25" plywood.

On one side (separate rooms) - Gym - 200 sf - Cork?, Media Room - 400 sf - Carpet?

Other side- Single room (Pool, poker table, Bar, lounge area) 600 sf - Engineered hardwood

Comments appreciated. Thanks in advance