If you mat all entrances, inside and out, you'll cut dusting and vacuuming in half.
Once your matting is down, always DUST FIRST!
Some people will argue that if I dust first, then vacuum, it blows dust on everything I've dusted.
Trust me if your vacuum is in that bad a shape you're wasting your time doing either.
Good vacuums with a decent filter bag and clamps won't leak and spew dust over cleaned surfaces.
A vacuum must be maintained. If you dump the bag frequently you'll spend a little time emptying instead of a lot time wondering why the vacuum isn't picking up like it used to.
Dusting is scraping dirt. If you vacuum first, all this litter ends up on freshly vacuumed floor.