I was able to find a large format (either 16"x20", or 18"x24") Italian ceramic tile that looks like marble, and was on clearance.

Carpet is awful.Your house will be 1000x more appealing to most buyers if you replace the flooring throughout with a hardwood, porcelain tile, ceramic tile, or even laminate that looks like wood.Some people do prefer carpet in the bedrooms which I understand.

Hi @Matt BrowningNo repairs were needed at the time of purchase, but some items were very outdated (house built in 1996 - contemporary southwest style - think brass everything and faded pinks, off white ceramics, and oranges).

It's a ceramic double sink. 

For 99c per sqft, I just do ceramic or porcelain tile DIY.

This will typically be about a ten year fix, due to the flexing mentioned above, and deterioration of the surface from improper abrasive cleaning. 2) Gut to the studs, install hardybacker board, medium quality American Standard cast iron/porcelain tub, and ceramic tile surround (without niches for soap dish or shelves- these are always the "weak link" in surrounds and are typically the first area to start deteriorating).

If a rental, I would also suggest ceramic at that price point (tile failing seems More like a DIY from past occupants). 

My Question is... am i better off putting it on top  of this Old 1"x 1" ceramic tile?  

Better products might use ceramic beads.

lvp now,  ceramics on concrete foundations,I had a lady ruin 2500 sqft of laminates with a sponge mop.animals and carpet don't mix. hardwoods need refinishing from wear. there's a reason Walmart's are using vinyl plank in the walkways of there carpeted areas. they seem to be wearing very well.