I'd choose a light floor to compliment the walls, like White Birch or Maple.

Mid Century Modern basement with cedar walls would look great with:

Slate floors (photo below is a basement in the Hamptons). Slate is not that expensive. I know two people who used MSI black slate (or blue slate) tiles and they said that the tile was incredibly easy to install (gauged slate - it had consistent sizing + a lot of honed pieces = smooth). They have tons of different sizes + a patterned one that combines various sizes. It runs between $3-4.50 sf. It is from Brazil = very durable and not slippery.

MSI slate - this was from HD's website:

Here is a customer's photo of MSI slate tile (12x24) from HD:

Terrazzo flooring would work well (my understanding is that there is faux terrazzo flooring that isn't expensive + looks nice).

There is some more modern terrazzo flooring that has a more subtle look to it:

Some people have used cement flooring in mid century modern homes:

Slate would be perfect .Wallpaper not so sure about. Is tha wallpaper mural or something they had done by hand ?

I'd choose large format slate and then use area rugs to define the areas.