Be sure and pull any necessary permits for the construction. These may require construction plans and diagrams. Also, depending on the configuration of your basement, you may not be able to put a true bedroom down there if there is no means of egress through a window (fire code). When you go to sell the house, essentially you couldn't call the room a bedroom.
For the electrical, think long and hard about what you want. Maybe it would be a good opportunity to run other cables as well. CAT5e or CAT6 for ethernet and phone, double coaxial cable, speaker wire, HDMI and/or component video, etc. Running wires after the sheet rock is up is a huge PITA.
I would consider hiring someone for the sheet rock. While it may save you some money by trying to do it yourself, the quality of the work likely won't be what you would ultimately want or expect, and it is going to take you 10 times longer than a professional. I've done some sheet rocking, and it isn't fun or easy. A professional crew will have the sheet rock in place, taped, and mudded in a half day in that basement... If they use the newer quick drying mud, they may have it sanded and ready to paint as well, all in one day.
Laying the flooring (non-carpet, either wood or tile) is something you could DIY. Just make sure and read up on how you would need to treat the existing concrete. For instance, for wood flooring you would want to lay down a coat of epoxy to act as a moisture barrier. For tile, you may need to pour self leveling concrete (this could be done before framing). Also, installing baseboard, doors, door trim, etc, is all fairly easy DIY stuff that will save you $$$.
Good luck!