If you have not done this before, this is a normal human reaction ;-)
Drywall is typically about $1.50-$2.00 per sqft of drywall (not floor). Depending on how many walls, rooms and closets you have, you might have about 3500 sqft of drywall in a 950 sft basement (I am guessing). Large flat walls are cheaper than small areas with lots of cuts & corners.
It will take a small crew about 7-10 days to hang drywall, tape and mud, then let it dry a day or two, then sand, mud again, dry again and sand again, finish and clean up. You may want to include texture and primer. That's a lot of labor, do the math.
A word of caution about cheap work.
If you have cheap capenters (aka handyman) do the framing, the surfaces will not be flat and sqaure. Bring a large carpenter square to check their work. Pay attention to soffits, boxes around ductwork and pipes and to the straightness of walls. Best to do this after the first day, once it's all done, it's too late.
If the carpenters do a hack job, it makes drywall more time consuming as they have to shim and bend. If the drywall is not square, it will cost you later when you install doors, baseboard trim and hang cabinets. You will see gaps everywhere, which need to be caulked, which makes you final product look like crap.
There is a great book on BP from J Scott about estimating cost. He did a lot of work in Milwaukee and his numbers are pretty good for our market. Cost of labor and marterils have gone up a bit in the last three years. I feel like I am paying more than double for lumber and millwork...
