Which of the newer Playstation models is best suited for a physical media collector?

I'm creating a physical media library. My goal is to have my favorite games in disc format and be able to play them offline for the rest of my life (so long as my hardware lasts). I understand some consoles and games require initial downloads, so I don't mind being online for that. But I don't want to be required to stay online while I play or hop online occasionally to verify my access. Is there a Playstation that allows for this? I already own an Xbox 360 and a Blu-ray player.