A potential problem with building walls in a basement is shifting of the concrete floor or slab due to expansion and contraction of the ground. This can can be a particular problem in places like Colorado because of bentonite, a mineral that is very expansive when wet.
I used to live in Colorado and refinished my basement. The proper method of wall contruction there is to build a wall frame of 2x4s, making it about 4 or 5 inches shorter than the distance from the floor to the ceiling. This frame is then hung from the joists. Glue a 2x4 to the concrete, the same length as the bottom of the frame and directly under it. Use a product called Liquid Nails to glue it to the concrete. Then drive large 8-10 inch spikes (available at any local hardware store, they will know what you are talking about) through the bottom of the frame and into the 2x4 on the floor. Predrill the holes in the frame for the spikes, to allow room for the spike to move up and down as the floor, and the 2x4 glued to the floor, moves up and down. This keeps the frame from moving laterally, and allows the concrete floor to move up and down without buckling the wall. When you dry wall, leave a gap between the bottom of the dry wall and the concrete floor. This gap will be hidden by the baseboard. Do not screw the dry wall into the 2x4 on the floor, just into the floating wall frame. This allows the floor to move without cracking the dry wall. Even with all of that, I ended up with a few minor dry wall cracks along the base of the walls after a couple of years.
Your local home supply store, like Home Depot, should be able to help, and may have how-to brochures available.