There used to be a Sony website that let you type in a game and told you what models had issues with the games that pulled up and what the issues were with those games.
All I can find now is this one which just gives the hardware revisions themselves. Basically anything that was an original 60GB model will play 99.9% of the games perfectly. The 20GB models also had full compatibility but no wifi. The 40GB models up to the MGS4 one included backwards compatibility(the MGS4 bundle that includes a black PS4 does, the one that includes gun metal grey does not.)
https://support.us.playstation.com/a...-PlayStation-3