Hi, Mike. If you put drywall directly up over the knotty pine, you will have problems around the door and window jambs. Believe it or not, it should not be that much problem removing the knotty pine. Get yourself a buddy or two and a couple of Wonderbars and it will be done in no time. The biggest problem will be getting rid of the old wood and carrying it out. Be careful of the old nails.
As far as the ceiling, this is somewhat a matter of choice. Usually, there are some things in the basement ceiling that you have to get to eventually and you never know when you will want to run another electric circuit, phone or cable TV wire or something. The best choice is probably a suspended ceiling. If you do go with drywall, you will have to box around areas that you know you will have to get to like plumbing valves and traps.