There are a few Final Fantasy games available on the Playstation 4 right now.
Final Fantasy XIV is the MMO. Very well done if MMOs are your thing, plenty of content and the story is actually pretty engaging. The expansion, Heavensward came out this year, and did a great job of introducing new classes, dungeons and story.
Final Fantasy Type-0 is a HD port of a PSP game of the same name. The PSP version never was released outside of Japan, so this is the first time the game is getting an official english release. It is good, but the story can be very convoluted, and being a HD remaster of a handheld game, some of the graphics and gameplay systems can be hit or miss. rent if you can to get a feel for it.
Final Fantasy X/X2 HD is another HD remaster of the Final Fantasy X series, originally released on the PS2. The games still look good, and are prob the most traditional Final Fantasy experiences available on the PS4 right now. Turn based exploration is what to expect with these games.
Hopefully this helps.