As far as drywall should we use the greenback drywall or regular drywall. And should we use the tripple coated screws or standard to secure the drywall???
Since you are screwing into Pressure Treated lumber framing, you should use some kind of galvanized, stainless, or coated screws to avoid the screw reacting and corroding due to the treatment of the lumber.
The most cost efficient screw would be the gray coated screws at 1 1/4" length, found in the exterior treated screw section at any large HOME IMPROVEMENT store chain.
I would not bother with 'green board' (Moisture Resistant board).
It seems that you are highly concerned about moisture in your basement. So, you might want to consider 'XP board' or 'Densarmor'.
If you are concerned about moisture...I would recommend waiting until you have some rain to see how damp the basement gets. Take a small piece of plastic (12"x12") and tape the edges down on the floor and/or wall. After a day or so or humid or rainy weather, check and see if there is moisture underneath the plastic. If there is, you have a damp basement and you may need to investigate and fix this problem before you begin your remodel. If not, then standard drywall should be okay.