PS2 Slim or Fat?

I want a Playstation 2 to play ps one and two I got all the stuff I need for it just Not sure what type the Slim or the Fat PS2?

Im pretty sure you can play rom right from the memory card slot now also is it faster reading a rom from memory card slot or Sata Ssd HD prolly like a 1TB Or 500GB what ever!, so I geuss what im asking is ps2 Slim or Fat and witch is faster the memory card port or the Hard Drive?

Thank You Kindly! Kyle Jump