I live in southern Wisconsin, and am refinishing the entire basement.I believe I have moisture issues dealt with.

I want to choose insulation that will 1) give me a good R value (at least R10, from what I gather), 2) minimize possibility damage if there is any future moisture, as well as 3) allow Romex to be run in the wall cavity.

With these critical issues out of the way, I'd prefer a method that is less deep, to save space in the room. And obviously, all things being equal, I'd choose a less labor-intensive method--putting up sheets of foam board, then furring strips over that, securing to concrete walls, instead of having to cut foam boards to fit between studs.

I've appreciated all the thoughtful advice I've seen here. I'd welcome any ideas.

Pretty much what you gain in space by using thinner insulation, you lose by using furring strips, so why not just frame a 2x4 wall and use R-11 or R-13 fiberglass insulation? And if you're worried about moisture, use at least a pressure-treated sole plate, and paperless gypsum board.

Always use your home ventilation system to control moisture. In a typical home, over 20 litres of water are added to the indoor environment every day. That’s 7,300 litres in a year, enough to fill a medium-sized swimming pool. Bathroom fans, kitchen range hoods and packaged ventilators such as heat-recovery ventilators are specifically installed in your home to help you control moisture and contaminants. Regular use of your home ventilation system will exhaust excess airborne moisture caused by bathing, showering, doing laundry and cooking.