Waterproof Basement

You need to treat the mold problem before you finish the basement.
No reputable finishing contractor will do the job for you if there's mold or water present.
If you do the band-aid approach and the water or mold comes back you may not know it because it will be hidden behind the finished walls and flooring, turning the basement into a death trap.
Drop the money and get the water problem solved now by a professional who can tell you where the water is coming from and the best way to solve the problem.