If your floor got damp when it rained, you need to address that issue before you even think about putting down new flooring. My first guesses would be a bad seal/old wornout sealant between the floor and the wall around the perimeter. My second guess would be a deteriorated or missing vapor barrier below the home. But I am no expert! For all I know it's leaking down the interior of the walls to the floor, which can happen if you have no overhang.

Ceramic tile floors are lovely and easy care, if you don't do light grout. Light grout gets grubby in a hurry. But ceramic tile floors are unforgiving if you drop something on them; if the object doesn't break the tile may break. But tiles can be replaced if you keep a few spares.

If you choose tile, be sure to do the tiresome leveling and laying down of cement board first. No matter how solid and level you *think* your floor is, the tiles or grout will eventually crack because there is no flex in tile, and there is in a regular subfloor.