Use a vacuum cleaner instead of a broom or mop.

As graywings recommends, I have used a vacuum for years for "sweeping."

I use a broom where my vacuum won't reach well (around the perimeter of the room and under or behind things, then use a vacuum for everything else.

One of the little tips for using a broom is don't sweep so vigorously that you pull back a portion of what is clinging to the broom with the sweeping motion, and to tap the broom on the floor to help release anything clinging to it after each forward sweep motion (sweep - tap, sweep - tap). And perhaps shorten your sweeping stroke/reach. This is especially helpful if your broom has newer style "shaggy" bristles (man-made material) to help collect debris, rather than a natural bristle broom, with smooth straw.

-Grainlady

As above, I sweep then vacuum. That's the only way to get most of the stuff. I often do a damp mop after a sweep then a vacuum up of the leftovers. That works well for the debris that is removed mostly by moisture. In the bathroom I always sweep and damp mop to catch as much hair as possible. .