You will get many suggestions, but let me start you off with one at the cheaper end of the spectrum. I installed Home Depot outdoor carpet 4 years ago and it is holding up very well. We fish, ski, tube, wakeboard... both fresh and saltwater. Fish blood, scales, sand, mud all seem to clean up pretty easily.
There are only a small few carpet mills left in business these days so all the retailers are getting it from the same places. What ever you chose look for the weight and backing. On a fishing boat nothing more than 16oz carpet is needed. Anything heavier just adds weight and holds more water which again means more weight.
The HD carpet I use does not have the rubber backing. However, it is thick enough to be comfortable on bare feet, but thin enough to dry quickly. I hose it down after most fishing trips and it gets soaked during every wake-boarding/tubing trip and have never had any lingering moisture issues.
I bought a decent grade of Overt0ns marine carpet and it's not holding up as well as I well as I had hoped.mif I were to do it all over again I would buy the vinyl sheeting like comes in a new tracker. I would bet that it will last forever while protecting your decking at the same time.