The combination of the plastic/weed barrier and mulch will help retain the moisture that we do get.

And $0 for roof, so where is the moisture coming from?

With all that said, slugs indoors is probably an indicator of something else, moisture related.  

Properties in locations with a lot of moisture require more maintenance than properties in dryer climates.

They also had a plastic moisture barrier laid down, but over the 2x4s (directly under the wood flooring.  

There are some moisture barrier treatments which can be applied to basement walls.

If they are not opening windows moisture is going to be trapped in the home and cause mold.

It's not so much a question of what is better - laminate or vinyl (plank or sheet), but what types of flooring are applicable to your situation.While quality laminate (AC3 - AC5) offers a "good looking", functional floor for the price, it does not handle moisture well and can be noisy for tenants below (depending on the sound deadening measure taken in the floor/ceiling boundary).Vinyl tends not to mimic wood as well as laminate {if that is the look you seek}, but it is non-organic, so a good fit for humid or wet areas (bathrooms, laundry rooms, basements, direct over slab, etc).  

For most people this is a geographic area near where they live and the easiest to penetrate because you are constantly passing other houses on your way home and know people in your neighborhood.  

But before that and if the floors have a decent finish (so the cat urine is not absorbed and penetrated) you might try cleaning/sealing the walls and other porous surfaces first.