People like to use bed liner, me I personally just use spray paint. I think it is way easier to clean as well as touch up, plus I have never been convinced that roll on bed liner is nearly as tough as the manufacturer says it is. I had it in one of my other vehicles and with in a couple months under the gas pedal I had worn through it. in my opinion, spray paint is 1/100th the cost, easier to touch up/clean, and just as durable.
With that said, I have a friend that had a lineX business, and about 12 years ago, he did his YJ tub, His wheeling is limited, but does DD the jeep often, and it has held up 9 gazillion times better than any of the roll on products, but ease of cleaning it is still an issue.
As for carpet, I would remove it as it would retain any moisture in close proximity to the floor boards. long exposure to moisture promotes rot, if the metal gets wet and is allowed to dry fairly quickly, Rot will not be an issue. To add, this is my thinking as it applies to a jeep where the carpet is loose fitting and contaminants (like dirt and sand) can get under the carpet and erode the paint. In a Pickup for example where under the carpet is sealed off, this is not so much a concern.