I've had it all: nothing, drop-in liner, spray-in liner, carpet, and mat.
I had carpet when I had a cap. With a cap I never had water in the bed but I've never had a tonneau that fully sealed (soft tri-fold, hard tri-fold, or fiberglass "lid"). They all allowed water into the bed to varying degrees so I would caution you about getting a carpet. Weather resistant or not, once the carpet gets wet on/in/under it, it takes awhile for it to dry (at least that was my experience).
My favorite combo was bed liner, rubber bed mat, and a soft tri-fold. I wanted to have a non-slip surface so stuff didn't shift around back there when I drove and I was only looking to protect things from the brunt of the weather. I didn't care if some water/dirt/dust got in there, it was more important to me that it didn't fly out of the back on the freeway and I could remove the cover in a couple of minutes (or re-install it) and toss it in my garage when I needed to.
Some of it will come down to budget for what's worth it to you but my RAM was the first time I had a spray-in bedliner...now I'd never do anything but a spray-in.
Just my .02