Why is the slab damp?  Carpet, is rarely a good solution over concrete. 

There are insulated subfloor panels that can be used as well to have a finished floor installed over top. 

I seocnd the White vinager method. That is how i clean my own hardwood floors. 

We follow the advice of one of our trusted wood flooring subcontractors in Charleston, South Carolina - using a white vinegar solution is the best way to clean beautiful hardwood floors!

Follow these simple steps to keep your hardwood floors clean:

- Vacuum or dry mop the floor to remove any surface dust or dirt

- Fill a bucket with a solution of 1/2 cup of white vinegar to one gallon of warm water

- Immerse a mop into the solution and wring out until it's damp-dry

(**Never use a soaking mop on hardwoods**)

- Mop the floors starting in one corner and go in the direction of the floor boards

- Rinse the mop head frequently and change the solution if the water begins to dirty

I think laminate floors denver is a good option for flooring while their is pets in house.

If basement ceiling is unfinished or has drop ceiling you can usually run 1 1/4" screws from underneath.  It is best to have a helper finding the squeaks and try to measure from the outside walls in order to find proper placement of the screws.  Top nailing the boards is a temporary fix at best.  

I have a mother-in-law that has been breeding dogs for many years and she swares by ceramic tile.

Laminate are durable but make the tapping noise from their nails when they walk on them.