This is how I brood ducklings, using 2 big wide plastic bins, a plastic tray and about 8 old beach towels. Spread the towel across the bottom of the bin. Raise one end of the bin up a few inches and put the plastic tray at the low end. A lid from a plastic shoe box works well for a tray. Put the waterer in the tray, the food in a bowl on the towel, and set the lamp near the high end.
Tipping the bin helps keep the spilled water at one end. The tray also helps keep (some of) the spilled water contained. The towels get changed at least once a day. Some folks run them through the washing machine, but I prefer to hang them on the clothesline and give them a good hosing, then let them dry. With 6-8 towels I can have a clean dry one ready to replace each time. And having 2 bins allows me to give one a good hosing & let it air dry while the other is in use.
No other type of flooring or bedding works as neatly as old towels for ducklings & goslings. You can use up your old threadbare ones or buy them cheap at the thrift store.
Being in South Florida also gives me the advantage of putting the ducklings outside during the warmest parts of the day. Once they're about 2-3 weeks old they go in a bottomless but covered pen in the grass to leave their mess outside. I still bring them in by nightfall to stay in the bins until they're old enough to be all feathered.