I had mine down in a finished basement. I didn't have as many as you are going to have, but here's what I did.
In a corner I laid down an extra large heavy duty tarp, spread it out on the floor, and taped it up the sides of the walls about 2 feet. I then took some plywood and tables I had laying around to make the other two corners and taped the tarp up those sides. I had some old linolium, laid that on top of the tarp and put wood shavings on top of that. (btw I used the corner closest to the door outside.) I basically used the deep litter method.
You're going to have 20 ducklings in your basement for about 6 weeks or more straight. They are going to get big during that time, a lot bigger than you might think and lay a lot of waste. I would give them a good amount of space.
Your biggest mess will come from the feed and water. Even if they can't splash in the water, they will make a mess of it. They shake their bills with the feed and water in it and it goes pretty high.. one of the reasons I had tarp up the walls. They will also turn the food to mush and the entire area around the feed area into a yucky mushy area. Feed spoils easily when it is wet so you're going to want to stay on top of keeping that clean... more so than their waste imo. I would keep their feed on the opposite area from the heat lamps that way they will have a cleaner sleep area. As they get bigger I would separate the feed and water areas. Keep both inside of some sort of container so you can try to contain the mess.
If you don't want them on the floor, rabbit hutches can make good brooders. You'll need several though in order keep 20 ducks as they grow. You'll find they are easier to clean also. Just make sure to put some bedding on one side for them. I see rabbit hutches for sale pretty cheap out here. I don't think you can keep them in rabbit hutches for the full 6 weeks though. Silver Appleyards are a heavy weight breed of duck.
Some people use kiddie pools as brooders, so that's another option. I've seen some people connect kiddy pools. One is a brooder, and the other is for eating and drinking. Maybe with 20 ducks you could have three of the larger kiddie pools connected up. Two as brooders, and one as feeder, waterer. When they get a little bit bigger you may be able to give them some swim time in the eating/ feeding one to encourage them to preen.
Welcome to the land of ducks! You're gonna love it at first. Then it will become a chore until you can get them out of the house, then you will love it again