The PS4 does not recognize/play PS1/2/3 discs. It does not even allow you to download older PS1/2/etc. games from the PSN (unless they were ported to the PS4, as is the case with a couple PSN games for PS3). However, Sony bought a company a year and a half ago called Gaikai that does streaming gaming stuff (like OnLive) and they are working to make PS1/2/3/etc. games available to play through the internet on PS4 (and also PS Vita and PS Vita TV). This technology is already used as the basis for PS4/Vita remote play. They have not announced how exactly this will work, whether games you own can be read from a disc to verify you have the game and streamed from a server or must be purchased through PSN to work.So currently, the PS4 does not support backward compatibility. The only current console that does is the Wii U, oddly enough, but only for Wii games and not GameCube games. Microsoft is supposedly working on a similar streaming solution to get Xbox and Xbox 360 games on the One but they haven't announced anything remotely official on it. Sony's service should debut next year.For the price of a refurbished PS3 and the cost of used PS3 games, you might as well get one instead of a new PS4.
Any game that is available for the digital upgrade plan is pointless to buy, honestly. The PS3 and PS4 versions of games cost the same ($60) and any saved data does not transfer from one version to the other. The idea for the upgrade was for people to buy a hit game on a current console ASAP and be able to move it to the next-gen console when they finally bought a new console, but that only seemed to matter if you were completely incapable of waiting a few weeks for the next gen version and console to come out.