If you use tripoli and rouge, it will get everywhere anyway. I put
my polishing set up in a closet with a curtain in front. Works
pretty well. Also put a cheap rug on top of the supposedly good
rug the apartment provides.
Oh, definitely, I'd planned to put something down. I actually use
Luxi when polishing, since I've found it's so much cleaner than
tripoli, rouge, etc.
They really do get everywhere.