I had carpet and kitchen flooring like yours.
I tore it all out!! (And discovered the carpet installer had a love affair with the staple machine and he (or she) put down a staple almost every square inch!!)
After getting up the carpet and thousands of staples, the removal of the kitchen floor was easy - heat it with a hair dryer on high and just slowly pull it up - and toss it away.
Now - choice about new floring - I selected 'engineered Oak' - a laminate of real oak on top of a substrate that provides stability. I purchased 3 inch TIG (Tongue In groove) from an online discount place and had it delivered. YES, it was a slow process to get it all installed properly, but it looks GREAT!! (Installation sequence pics are available on request)
Downside - the slide rollers make a 2 inch wide indentation in the wood! When the slide is in, it does not show - when the slide is out, we cover it with throw rugs.
