When I have a situation with mold, I first eliminate any source of water or moisture. 

So, my floors have been a concern due to moisture and cracking.  

Carpet is the cheapest and will look fine, but if there is any chance of moisture down there I'd avoid it. 

As mentioned before, the risks of tenants moving their own appliances, causing damage, getting injured in the process, or improperly installing (think gas range leak) is another liability to worry about.You can easily buy low to mid end set of appliances gently used or new at a outlet type store for less than a months rent, which would have likely prevented or shortened your vacancy time in this case and thus payed for itself.

Here's a resource for buying previously owned/gently used guru stuff.https://www.ebay.com/sch/successguys/m.html?

Placing them properly as well as resealing when necessary will deter moisture and water issues in the future.

We do annual, gentle increases on longterm tenants-because they expect it.

Some parts had turned wavy because of moisture I think?

My only caution with laminate is that moisture/water will damage it...so keep away from wet areas.If you do replace with new carpet, make sure there is a clause in your lease requiring the tenants to have the home professionally cleaned when they leave....or there is a charge to do it for them.Hope this helps!

I havnt seen any water but I am afraid to do anything like carpet until I know if there is moisture.