I took my little chick waterer and placed it into the flat part of a paint roller tray. I lined the slope with a textured shelf liner to give them traction to walk down the ramp to the water. They could splash all they wanted and the mess fell into the tray. From there, they graduate to a larger waterer placed into a kitty box.
Then when they're big and they go outside, I have a woooden frame covered in hardware cloth on one side, and a plastic tote that sits inside the frame. Place a 1 gallon waterer on top, they can splash it out and the waste water and excess food spills into the tote, out of their reach. Easily clean up and dry bedding. I measured the wood frame to fit snugly around the tote. It's about 10 inches off the ground, but by the time I add bedding, it's only a 4 inch step onto the platform. I was amazed at how much water was getting in the pan... no wonder the bedding was gross after only a couple hours.
They need access to water deep enough to stick their heads in and clean their noses. Finding a way to contain the mess water will help keep things cleaner longer.
I use old towels as bedding since I can rinse, wash, dry, re-use. They're absorbent and safe, and I don't have to buy them over and over to keep them clean and dry. For the last batch of ducklings I built a brooder with a wire bottom. First week, towels on the whole floor. 2nd week, towels on half of it, and a plastic tote under it to catch spill water and food. Then a towel on only a 1/4 of it, a sleeping pad I guess you could call it, and another plastic tote added under that side. I could pull the tote and dump the waste outside on the compost pile, hose it out, fresh and clean and nothing to continually buy for cleaning besides Clorox clean-up spray. For the first time I used one of those "deep dish" dog waterers, since I had the wire bottom and plastic tote below, I wasn't worried about how far they could throw water. They could clean their noses when ever they wanted. Granted I had to refill it 3 times a day with 10 ducklings... but they loved it.