Are you are getting water in your basement? If so, you will have to get the water problem fixed first before putting in ANY flooring. Otherwise, you will have the possibility of a mold infestation, no matter what kind of floor you have installed.

Ceramic tile, epoxy and luxury vinyl floors (LVF) are all great choices. Ceramic and LVF's cost more initially and can withstand water better than most floors. Carpet is the most comfortable and the easiest to replace and move on. However, a disaster is a disaster - most floors will be replaced anyway and hopefully you have good insurance coverage. Ultimately, the choice is yours!