Question about Final Fantasy games (VITA)

Try out 4, 6, 7, or 10. Those seem to be the most accessible ones. Personally, I'd start with 6.

They are all unrelated. Search the internet for "best FF game" and read one of hundreds of thousands of comments about people's personal opinions.

If you liked the original FF1, get that then, but get the FF Origins version or whatever the remake is called. It has some updates and bug fixes.

VII, VIII, IX, X, XII

While many of the earlier ones are deemed "best" by the core fans.
A lot of players that rolled into the series later on will say that X/X-2 etc are better and so on.

So it depends a lot on personal taste and how well you can stand older games in terms of graphics and gameplay.
I would suggest you start with the earlier games and then move ahead as this would make the transition in graphics easier.
Moving from FFX back to FFIII could be a bit hit.

Also as pointed out, they're largely stand-alone. Don't feel bad if you skip one of the earlier ones for your own reasons.

Personally, while I loved 7, 8, 10, 10-2 etc - I'm very partial to the Final Fantasy Tactics games. I just really like the game style.
Also, when you're done with Final Fantasy - there are plenty of other JRPG's you could look at.

Whether its the Persona and Shin Megami Tensei series, Dragonquest, the Atelier series, Star Ocean or any number of others.
.Hack// can also be particularly enjoyable. Obviously these games span across a wide range of platforms. So I don't know which you'd have access to. But many of the series are worth checking out if you enjoyed Final Fantasy.

I would really suggest you start with the old-school ones. FFVI probably has the deepest story of them all. FF I & II was a bit too basic for my own taste, but it's a good and "easy" introduction to the series. Note that I played them way later than I played some of the other games.

Once you start getting to the 3D versions you're going to hear a lot of varying opinions on what's the best one and what's the worst. It's also a matter about where people were introduced to the series. If FFVII was the first they played, that's the one they love the most. If they started before that, the risk is likely they think FFVII was a step down quality-wise when it comes to the story.

I personally got emotionally attached to VIII, but not a lot of people agree with me. I found the story in that one the most beautiful of the games, even if not the deepest.

6 is my all time favorite.
I hought 2 was cool too, but the whole skill-based levelling thing isn't like any of the other games in the series. If you want more like that, you should continue with the SaGa series.
And I have a soft spot for 8, because abusing the Junctioning system is just hilarious. (Yes, I've one-shotted the final boss with a lvl 7 character once. woohoo!)

the fun starts after FFIV with FFVII,FFVIII,FFIX the best 3 of them
of cource i'm talking about the original releases and not the remakes(i haven't played) of the early Final Fantasies
personal favorite FFVIII,Squall kicks ass