Our wash floor and drain trench were just untreated concrete for 35 years of heavy use. Unless you're going to acid soak rugs or use some pretty caustic alkalines you shouldn't need to coat your floor or trench.
After moving a large piece of equipment we found a couple large cracks in the drain trench that were caused by building settling. I decided that either Line-X or Rhinolining would do the best job of sealing and be impervious to anything that would go down that drain. Line-X in our area would not work on-location, so we had it coated with Rhino. Four years and it has been perfect; I would recommend polymer coating for this purpose.
The wash floor also had enough cement washed away to expose the aggregate to the point of losing the rock. We were going to either skim coat it with a modified cement product or knock the floor out and pour a new one, but the Rhino guys said they could coat the floor as well, and promised it wouldn't be slippery as they had coated the decks of several commercial fishing boats. The applicators didn't do a good enough job of cleaning deteregent residue off of the floor, as we've had a few bubbles. That's when we found out Rhino doesn't stand behind their applications on anything but truck beds. We have had to cut the bubbles open, clean and dry the floor under, and glue the material back to the floor in five or six spots. Other than that, 4 years of use have had little effect on the floor. It was slippery as ice when new though, and I had to find a topcoating to give it a little grip so guys could work without getting hurt.
Also, after years of epoxy coating the underside of our rug washer and having every bit of epoxy fall off and have to recoat every two to three years, we coated the underside with Herculiner. No more problems.
Check with the material manufacturer to see how long they recommend a new floor cure and what the moisture level should be before applying anything. Go with Line-X if you're going to coat the wash floor. Get the applicating company to put their promises in writing.