Tips for starting out a basement finish

http://imgur.com/a/QkBkL

I purchased a home with what I consider a "semi-finished" basement. I don't mean that in any technical term, just that the following are true:

• The house is pretty new, and the basement area is clean
• There appears to be some type of insulation over all the walls which keeps the basement pretty warm, even though it's like 10 degrees (f) outside.
• There is electricity already, and power outlets that work
• There are two heating vents hooked up to ducts which provide heat.
• I can spend time down there already, but my wife won't because it's ugly and concrete is not fun to walk on.

I would like to finish it, and I have a bit of extra cash to help me do it - maybe one to two thousand dollars. I'm not looking to do anything crazy, just put up walls and a floor to create one giant room with carpet that my son can run around in. Maybe throw a TV and a couch down there, but mainly I just want a giant play room. I don't plan on putting in a bedroom (although there is an egress window), and I think there might be plumbing (see picture two in the album?), but I don't plan on putting in a bathroom either. For now, just walls, a floor, and a ceiling, and I want to do 100% of the work myself.

My questions are as follows:

• In terms of framing, I've watched quite a few videos on youtube and it seems rather simple if I follow instructions. I haven't found a single video or guide where someone is framing walls against anything other than concrete however. Since I already have this white insulation stuff up, can I frame over that? If so - how much space should I put between the frame and that insulation? Is there anything special I need to be aware of?

• I've laid carpet before and I did a DIY installation of hard-wood floors in my house, but that wasn't on concrete. Do I absolutely need something in between the concrete and my flooring? Moisture is not a huge problem as I live at 6,000 feet and it's pretty dry here most of the year. The basement is garden level, and with the windows open it already feels like part of the house, temperature and moisture-wise. It's running about 3-4% higher humidity than upstairs though, if that means anything.