Carpet in basements is a very last resort IMO. Look into tile of LVP, both are good options for basements. If you wanted carpet again do carpet squares instead, because then you can just replace the damaged ones instead of tearing it all out.

Carpet in basement seems like a bad idea any way you slice it, especially if you have issues with moisture and/or potential flooding. Vinyl flooring planks/tile would be better, but would still present opportunities to trap moisture coming from the ground, which you don't want.

If I were in your shoes, I'd go with terrazzo. Highly durable, low maintenance, and waterproof. Perfect for a basement. Not the cheapest option up front, but it'll still be there when the rest of your house has rotted away In the distant future.

And then you can put an area rug on it, which can easily be pulled up and cleaned if it gets wet/dirty.

If you have concrete under the carpet, would you consider polished concrete? It's a very industrial look, but they can add acid washes and dies to make it quite beautiful. And absolutely no issues with water. I wanted polished concrete and couldn't do it because 1970's tile had left grid marks on our concrete. We instead went with metallic epoxy in black and silver. It's definitely not for everyone, but I love it. Water gets in, something gets spilled, all it takes is a mop.

The least expensive, longest lasting, shortest install time and DIY friendly is epoxy paint.