I would recommend playing the older ones on a handheld for the simple convenience along with the lowered expectations for cinematic quality one has when playing on a handheld. I would recommend six.
After that, I would suggest going through the PS2 or latest FF.
Afterwards, if you liked the PS2 ones, go to the PS1 games. If you liked the handheld more, continue to go backwards from six. The PS1 was rough, so going back without having some interest or for nostalgia can be rough. Although, seven through nine had some fun experimentation on the battle systems.
If you don't like the gameplay so much, but you enjoy the world, you can also try out Crystal Chronicles or Tactics.
I haven't played either of the online versions.
After that, I would suggest going through the PS2 or latest FF.
Afterwards, if you liked the PS2 ones, go to the PS1 games. If you liked the handheld more, continue to go backwards from six. The PS1 was rough, so going back without having some interest or for nostalgia can be rough. Although, seven through nine had some fun experimentation on the battle systems.
If you don't like the gameplay so much, but you enjoy the world, you can also try out Crystal Chronicles or Tactics.
I haven't played either of the online versions.