Make sure you have easy access to escape incase of fire OTHER THAN your existing stairs!This is a must and should be your first concern,other wise all you are building is a possible coffin.
As for materials...well that is a matter of choice and what your budget allows.I have used wood and metal and they both do the job.
Metal is cheaper than wood(I find it easier to use than wood because I have worked with it alot and I know the tricks) but requires screws and a screw gun.Attaching trim and doors to metal framing raises a few issues as does attaching insulation.
Wood is the material I would suggest a DIY'er use because you can build and attach everything with nails and glue,and a saw and hammer are about the only tools you will need(don't forget the level).
I would insulate and vapor barrier all the exterior walls.
Interior walls and ceiling can be insulated for sound proofing.Luck