It's not a habitable space.

Code requires at least 7' below the finished surface to be considered living area. You could finish this off as an informal rec room, but it wouldn't be able to be claimed as additional square footage. It would be very expensive, but there is the possibility of having the floor lowered if you want it to be actual living space. As far as floor covering, you are probably best to go with an inexpensive carpet (you can get carpets with a foam back at most large home centers) that would just lay over the floor. There are also products available to skim over the floor to make it smooth so that you could lay tile.

I had a similar floor in my basement. I got several bids for 'self leveling' and sanding floor down so I would not lose ceiling height. The square footage is only 1000 square feet and the bids were all over 10K! FORGET THAT.

So I ended up using this product....

http://www.homedepot.com/p/Rapid-Set-55-lb-Mortar-Mix-04010055/202188453

with some friends and skim covered the lowest spots and holes, used a heavy duty chisel and hammer on the really high spots and then cleaned it all really well. I covered the floor in rubber interlocking flooring and it worked great. http://www.rubberflooringinc.com/all-tiles.html

What is nice about this rubber floor is it was super easy to install and if the basement has any moisture, it wont rot, is cleanable and you can replace one if needed and it was low profile so it did not further lower the ceiling. Carpet in basements are a bad idea.

Paint the Ceiling/ floor joists and walls white and then at least you can use the area for storage, crafts or game space...

This is a stock photo of the flooring

Use it for what people used to use basements for- store your apples, wine, bulbs and garden stuff.