"Best" is a relative term.  There are certainly options that provide different levels of comfort at different price points.  Recently, we've used a product called Thermal Dry from a company called Basment Systems that installs a over the concrete. It is a snap together PVC product (unaffected by moisture) that has a matte finish(for carpet) or a faux finish (like a wood appearance).  This prevents direct transfer of moisture from concrete to carpet and provides a (minimal) insulation layer at the floor layer.

I am sure there are other simlar products on the market, but this one has served us well.

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.  

Your best bet will be white or red oak. In any kind of wood, I would recomend you to do the finish coat with BONA HIGH TRAFFIC, is the hardest finish yo can put on your floors and is water base.

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.

Tthe squeaking sounds you hear are probably from movement of the boards, either against each other or against the sub-floor beneath the hardwood.  The nails used to install the original sub-floor may have barely missed the joists and are now rubbing against the raw wood.  The popping could be sudden movement of the ajoining hardwood boards. 

You may be able to top nail the hardwood in the joints between the boards.  A more effective solution would be to screw up through the sub-floor into the hardwood.  This will suck the hardwood down tightly against the sub-floor.  Take the opportunity to pull out  any visable nails that could be rubbing against joists. 

The second solution depends on access to the area below your squeaks.