I like greenboard but wouldn't go all around a basement unless I just had the money to spend. You may also need an extra coat of paint depending upon what you do to cover the green. I like to greenboard the entire bathroom but most new homes built around here don't use any greenboard in the bathrooms. Humidity is normal with basements and unless you have some abnormal moisture problems (and many do) then you wouldn't need it all the way around. There is a moisture test you can do on the wall and floor to see if you have much condensation. Basically get a 2'by2' or so piece of plastic or foil and tape it to the wall and floor sealed all the way around with duct tape. Check in a couple days to see if much condenses.
Greenboard is heavier(and to carry downstairs too), more dense, and the gypsum has an additive to it which makes it a stiffer board. It also has a moisture resistant paper. I like working with it better than the regular cause it seems like with the regular stuff, you bang the corners, dent the edges, tear the paper, and when your studs and plates (treated floor plates can measure 3 5/8") don't line up just right and you screw into regular board into the indented stud or plate, then it tends to break more than greenboard at those corner and edges. You don't have this so bad with green. You really notice the difference when you change from working with green to regular which seems so flimsy. I think the board better resists screwing too deep into the paper also.
Like I said before, I like it better, use it for sure all the way around in bathrooms (which is more than many do) and would seriously consider it all the way around in a basement but usually the entire cost increase is too much and except for abnormal basements, it is probably just overkill for which I am known anyway. $100 isn't too bad depending upon your finances and cause of the way you are asking, it appears you could afford it. And when you think about what moisture may do it over 20, 30, or 40 years to drywall, $100 to extend the life of it (like a second coat of paint) may be a cheap investment in the long run. Add in another light coat of paint that may or may not be needed.
It is a better barrier but I think I agree with our resident expert(the insulator) that if the paper is touching the drywall then it won't condense. To me, kraft paper would be plenty (although plastic is a better moisture barrier) but there are those that would still put a plastic vapor barrier on top of the paper (or by itself) behind the drywall but I don't think you need both. If you have much moisture through the wall or floors, I would spray it with a sealant but some would also say to put plastic on the floor and walls up to ground level but alot of that depends upon the water level in the ground(are you on a hill or next to the creek, etc.). All in all, I don't think you need to slit the paper but even if you did, it wouldn't make much difference. Moisture moves differently through ground in the basement than the air for floors above.
You should concentrate more on your air handling down there such as the furnace, duct work in each room, return air vents in each room opposite and a different level than the ducts, a/c, dehumidifiers, fresh air ventilation, etc. to get rid of the humidity. By the way, a lot of this depends upon climate and what may be good for Alaska may not be good for Texas. Check with what your locals do and lets see what other posters have to say. Good luck.