Anything you put on the osb will not cover, the osb color will bleed through. Unless you want to sand the shit out of it and prime and paint, still have all the seams. The best thing to do is 1/4 or 3/8 drywall over it and finish with joint compound, primer and paint. If you use the 1/4 inch stuff you may want to glue as well as screw it to the osb. !/4 inch tends to be a bit flexible, you dont want it to bow between fasteners. This is more of a problem on ceiling then walls so in your case not as important. 3/8 drywall is usually the same price as 1/2 inch. There is also a type of drywall out there called paperless, great for basements. Manufactured with out paper so mold has nothing to grow on...great for cave construction.
I used to do drywall and drywall finishing in a past career. PM me if you have any questions