The best floor paint, in my opinion, is oil based porch and deck paint (aka alkyd porch and deck, polyurethane porch and deck, etc.). You could use an acrylic , water based, paint but you should prime first when an acrylic is going over an old oil base paint. The oil based porch and deck will smell strong and remain a little soft for a couple of days, but it will stick good.
Since your floors aren't peeling this will be easy to paint. Here is what you need to do;
Clean and clean and…. Use TSP, trisodium phosphate, or similar cleaner to remove the dusty powdery paint residue. This will also etch the surface. You can use a shop vac to vacuum up the excess water.
Allow it to dry for a day. Running a fan could help also open up the windows. Normally I would recommend wiping the floor down with a solvent like Paso, but this stuff really stinks and you will have the paint smell to deal with. If you do a good job with the washing then further cleaning isn't necessary.
Now for the painting. This will be a two coat process. The first coat can be thinned a little, up to 25%. The second coat needs to be full strength. Painting is very simple. Cut in the edges then use a 1/4" or 3/8" roller. Just roll on the paint as a heavy coat and work it with the roller until it looks good. (Be careful, don't paint yourself into a corner.)
The nice thing about paint is you could use a neutral color for the background then paint patterns with an accent color. Adding another dimension to a rooms decor.