A stairway needs to have a 3-way light switch, by code, so you need to have the wiring for that in place before you start drywalling things up.
A stairway can also be a brutal drywalling job as there are lots of angles and corners and odds are the framing is crooked. Probably not the best place to start a first attempt at drywalling.
Even if you hire someone, you should study these 2 brochures carefully, especially if you are not pulling permits for the work, as most contractors will cut corners otherwise.
http://www.calgary.ca/docgallery/bu/...evelopment.pdf
http://www.calgary.ca/docgallery/bu/...ring_guide.pdf