I'll just jump in here really quick and make a small note since Final Fantasy is actually my favorite collection of games, and if you wish to play them, I'd like to give a bit of insight as to which versions are the best.
Many long time fans will says that IV-IX were the golden age of the FF games, and I would agree. After VI, you start to dip into the Playstation games that may or may not look aesthetically pleasing to most people, as 3D models aged pretty poorly. You'd have to decide whether or not that bothers you.
The older games like IV, V, and VI are fantastic. However, being able to play them on a proper platform (the intended versions or versions that stay true to their original design) is tough unless you emulate. IV is best played on the PSP/Vita as the Complete Collection, V can be found on the Playstation Network (you can also find it on Steam, but uses redrawn graphics that don't quite fit the aesthetic of the original), and VI can be found on the SNES/Playstation Network (you can also find this on Steam, but again, uses redrawn graphics that detract from the feel of the original).
Unfortunately, there aren't really any good ways to play V and VI in modern times, since they haven't been remade/remastered much outside of the Steam/mobile versions. Everything else has been a port from the Playstation/SNES versions, which suffer from bugs or massive load times. Usually the SNES versions are the way to go, which is why I say that an emulator is your best bet.
I think IV, VI, VII, and IX are all great. Each of them have a wonderful cast of characters with great music, atmosphere, and character development, and cover themes of sadness, loss, self reflection, and understanding of the self, each in their own way.
Seeing as I'm biased, I can't fairly recommend one to you. However, VI and VII are often regarded as the best, with IV and IX right behind them. VI is my personal favorite, so naturally I'd say that one.
Zloth pretty much nailed it in regards to VIII, X, XII, XIII, and XV. I liked the story of VIII and X. XII's story is a little all over the place, but the combat is pretty fun. Admittedly, I never played XIII or XV because they never really appealed to me. I've seen people play them, but I have a hard time wanting to play them. They're so different from what Final Fantasy was always best at.
