How about an inexpensive "area rug," could buy cheap uninstalled wall to wall carpet and leave it unbound to save $$$, or bind edges if you want it to look better?

Thank you. Now the questions:

1..To clarify, you meant to use the cut-to-size carpet as an area rug, or just to buy an inexpensive area rug, or to buy the cheap uninstalled carpet selection is still from the "cut-to-size" which is meant to be installed, correct? Or is there a section of carpet for me to just to cut to size?

2.."bind edges" means to use the carpet grabber with the tiny nails on a piece of wood (just like how they install the carpet) or to use the metal piece between the borders of carpet and vinyl sheets, or to "hem" like a sewing job to finish the edge of the cut-to-size carpet as an area rug?

I think the vinyl sheeting would be unwieldy to walk on. I don't know what kind of painting you're doing, if this would work for you, but I temporarily put down old sheets to protect the flooring while painting.

It's a good idea, yet I also have students coming over. They may trip themselves over the old sheet