Just wanting to interject: If you can play FF6 or Chrono Trigger, then you can play PS4. It's on that level and I highly recommend it. Easily the best RPG on the Genesis, one of the top for the 16-bit era and has aged super well to boot. Plus it covers the lore of the other 3.
If you're not interested, then you're not interested; just thought I'd try to sell it a bit. It's an incredible game.
Are the PSs like the FF series in that each numerical entry doesn't require knowledge of the previous?
They are not standalone games in terms of continuity, but Phantasy Star IV ensures you know the relevant details of the previous games, so you don't need to touch I-III at all except out of possibly morbid curiosity (they have aged far, far less gracefully than IV has).