1 is the first, should play it because
4 is classic as it is a very /classic/ in all sense of music, visuals, characters and "ehh overplayed trope!" but...well, thats like complaining about Tolkin using generic like fantasy elfs yo...ewww
5 is worth it if you like classes playing with min maxxing, using odd ball class combos to do stuff etc. 3 is similar but because it is older, more limited, so 5 is the better exp for /those/ type of players that want the class role fiesta type thing.
6 is to many, the prime and top of class of classic era JRPGs - if you play through 1-5, you will see how it all culminated in 6 in terms of the product they are producing, not the story, all the stories are separate.
Also, while not Final Fantasy, Lunar the Silver Star story is the classic of the classic anime jRPGs of the non FF-line. Everything about that game is just done so well. It is "such a generic trope!" but it all those tropes and classic things, done to the best and most well put together way. the PSX Complete version is the best imo.
Also, there is debate around about the best versions of the FF games, but the Pixle Remasters are the most accessible, and the best versions out side of small things - other than if you want to do the /full extended/ FF4 stuff, then the 3d version(s) are. To me the 3d version of 4, felt smaller of scale than the SNES one...merely because of perspective, the characters and voice in FF4 3ds are top notch and what they expanded is /some/ used in PR- but not fully, and if you are a fan of 4 in general and haven't, play the 3d one.