Yes, you have a problem! You didn't mention if you have poured or block walls. And what do you have for flooring? And is it completely, partially (what %), or not-at-all below ground? The answers to these questions, along with a reference to a related link (below), you should first solve your water problem before you finish the basement. If you're gonna make it a studio, you DON'T want to have to rip anything up to fix a water-related problem.
SO, w/o further ado, here's a link about Water in the basement. And, you can search the Forum's Main Page with your Browser's FIND Feature for words like 'basement', 'crawlspace', and/or 'water'. There's lots of chat about the subject. If you have any more ?s, post up. My best to ya and hope this helps.