surface idea for basement floor

Red Squirrel

My current basement floor is bare concrete with old hardened glue from a carpet that was there, and it is full of drywall dust. I can vacuum till I turn 90, but there will still be dust, it is embeded in all the tiny little crevises of the floor. It's not really smooth.

I want to resurface it on the cheap so I can at least walk on it without needing slippers to avoid socks from getting dirty. I was even thinking of just laying vapor barrier on it but it would be hard to vacuum as it would always get sucked up.

I've seen people put rigid foam then plywood on top, does that actually work well, or does it sag with time? In the future I'd like to put some fake hardwood (real kind not recommended in basements) or tile. But for now, I just want a clean smooth surface to walk on, that is also easy to maintain. Does not really need to be nice. I'm even wondering if that dri core stuff at home depot would be any good?

I was even thinking of painting, but the floor is probably too dirty for it.

Ron6519

They have tile cleaning machines with brushes on them that should work at cleaning the floor.
I use this one:
Hoover FloorMate Spinscrub 800 Wet/Dry Vacuum Cleaner with Tools, H3060
You can probably rent something similiar.
Put an ample amount of soap and water on the floor, let it soak in a good while and go over it with the machine. When you're done agitating it, you flip a lever and it sucks up the water.
You can also use a twin brush machine and a wet vac.
Ron