Hi Dan: Congrats on your new house. You are wise to have elected to have a deep basement. When finished, it will increase the living area of your house by at least 30% if not by 50%. You'll love it!
No, I would let that concrete cure for at least 6 months. Otherwise, you run the risk of taking chunks out of it when you set your anchors as well as not allowing it to cure as it should when you cover it. Just my bias, but I would hold off until May or June.
As I've mentioned in so many previous posts, painting the inside of the basement wall with anything will be temporary at best in retarding moisture. You should cover the walls with minimum 4 mil (8 mil is best) plastic sheeting. I used 1X3 lath laid flat to the wall, held by 3 anchors, using a roto hammer to drill the holes. Very fast. I cut 3/4" styrofoam insulation that I fit tightly between the 1X3's. 2X4's on edge is a good option also, but you will have to use 2 1/2 or 3 " gavlanized screws to hold them in. The one drawback about using the 1X3 is I had to use the small 5 cubic inch electrical boxes which can only hold a 15 amp duplex with 14 guage wire...not much room in there. If your slab doesn't have rigid insulation under it, then I would put down 2X4 PT sleepers flat over the floor with 1" rigid insulation between them, securing them to the floor with lead anchors, as they will need to hold the 2X4's down securely. Then you can put down subfloor over this framing then floor of choice over that. Personally, I don't like putting plastic sheeting anywhere where it is horizontal.....as its just begging to hold water on it or under it, which isn't good. If moisture is rising through the slab, I'd let it rise and remove it with a dehumidifier, which you will no doubt have in your finished basement anyway.