My favorite way to hang cages is from above (no solid parts underneath to collect poo/hay/hair).
I agree, while using other methods works, anything solid under the cage collects debris and is difficult to clean. For years, we simply put large nails in the vintage barn's oak walls at a 45 degree angle, two to three per pen depending on size, and hung the back of the pens directly on the wall. Back then, the nails and the cages were made of sturdy metal, and they hung that way for years without sagging.
That method no longer works, the nails bend and the cages are flimsy and droop, requiring rope/chains to support the front of the cages. I like the solution
@Alaska Satin uses. I've seen pens suspended from the rafters with S-hooks on chains (like the chain used on dog tie-out stakes) to attach to the four corners of the pens. It was so funny to see a row of four connected pens suspended this way, housing four albino white rabbits that were 'scanning', swaying back and forth in unison, making the entire row of cages swing back and forth.
I've had to make quick space for rabbits using simply sawhorses with 2x4 boards laid across front and back, and the pens placed onto the boards for support. It works, gets the pens up off the ground, but it sure collects debris where the pen meets the boards. It's good to be able to remove pens easily for cleaning, I prefer the single-rabbit cages for this reason. I have some wonderfully sturdy row-of-five pens that have lasted decades with no repairs ever needed, but it takes two strong people to mount and dismount the row--they're very, very heavy, made with extra heavy wire. And, you have to rehome all five occupants while the pen is down for cleaning.