Watch out for the slightest bit of damp. It will destroy instruments and studio equipment without mercy and is really bad for your health. If the walls haven't had a lot of money spent on tanking, or if the existing system is old, then you're asking for trouble.
Basements are difficult to sound proof and acoustically treat too. To stop sound getting out you need to build a room within a room, that is totally air tight and isolated from the structure with a floating floor and ceiling. For that you need lots of insulation, framing, resilient bars, a double layer of plasterboard, barrier mats/ damping and a sealed heavy double door. Being airtight poses problems for breathing so you need an acoustically designed ventilation system. Low ceilings are notorious for being difficult environments to record and mix in.
The basement may not qualify as a habitable space and studio use can invalidate home insurance. A lot of them are listed for storage use only. Are the electrics okay? Any modifications to the building can change your council tax band and can cause problems if you try to sell the place due to building regs (or problems for the landlord if he'd allow it). More than a few people will need an adequate fire escape which might mean having a second exit depending on where the main door is located in the house.
It can be a nightmare.