Well, I don't remember who said it, so I could quote them properly, but FF's are games that you had to grow up on. I don't think most people are going to get into them by playing the old ones on SNES and PSX, so VII RE and XV are probably the best points of entry, since ARPGs are the route the series is going towards anyway.
If you don't mind the graphical limitations though, I'll try to go through what I can. I've replayed all of them recently, in between free-time through working from home.
I-V are the hardest ones to get into due to the graphical limitations and how they play. Of those 5, I would say
V is the best one to play, since the Job System lets you fukk around the most.
VI is the most-modern version of the early games, so it's a fine starting point. Relic system is ... hmm. Let's just say while you're restricted to class, Relic gives you the freedom to make what you can through it. It's not hard to use but the stat values of the games are a bit fukked. Story-wise, the first half is amazing, while the second lets you chose how you go about it. Terra is more of a plot device than MC, so the game gives you a lot of freedom to pick who you like, while still telling a decent story. The music is

I recommend this, if you want to see how SNES Turn-Based used to play.
VII is the most popular entry in the series. I can't understate how big of a deal this game was. It was the only reason a five-year old me got his PSX. At the time FMV's were something none of us could imagine. It gets shat on now because of clunky graphics, favoritism from devs, annoying fanboys and how shytty everything that derives from the series changed what the original was about, but I still think it's 100% worth playing. If you play any of the PSX ones, this should be the one. It's the most popular one for a reason. The story, the characters, the villain are iconic. The music is Uematsu at his best. Sidequests galore. Some people say it doesn't hold up due to Lego graphics, but if you look past all of that, you get one of the best video game experiences ever. It's not even my favorite, but I can't object against the statement, "Everyone should play FFVII, once in their lifetime" It's up there with OoT as a must-play forever. Ignore everything that comes after this game. Cloud isn't an emo/edge.
VIII and IX are niche titles. I enjoy both, but you probably shouldn't play either of them. I LOVE VIII, but I can't deny that the story is fukking stupid. The junction system is laughably easy-to-abuse, like Shaq in Nba Live 2003- who could post up, shoot from half court and get rebounds from the Foul line. But I fukking love that game. It's like that cousin that you know ain't shyt, but he's always a vibe. This is Uematsu continuing banging out another classic OST. Triple Triad is one of the best sidequests of all the FF's. You'll kill time just breaking that game.
IX is... hard to explain. This is the one that people either really fukking love or really hate. It's a callback to the older ones, which I think makes it harder for newer players to get into. I can't like, I know I said I enjoy both, but I think the criticisms on this one stick out more than any one. The game is painstakingly slow to play. The plot is stronger than VIII (anything is) but it's not as fun as VIII. This is like the mid-00's Spurs of all the Final Fantasys: It's competent, does everything right without bringing in anything different or stepping out of its zone. I don't recommend you play either, just listen to the OSTs.
X is the next best one to play after VII. I think this is the easiest one to get into. This game is linear, but you forget that as you go through the game. Spira is such an amazing world and the characters help push you through why it's worth saving. Everyone is suffering, and every character has their own idea on how to stop Spira from suffering. It builds so much for a world we're simply walking from point A to point B. Anyone who complains about Tidus didn't really play the game. He starts off annoying but you get used to him quickly, and he comes off as completely likable by the end. The battling is fun. I can't explain it further, It's a different take on Turn-Based and you could switch to anyone. The movement is all streamlined and quick. If I didn't type enough as it is, I could break down the Sphere Grid and give it the respect it deserves, but lets just say it's one of the best and ambitious job systems in an RPG. This is as close as people will get to a WRPG's system. Music...

Wandering Flame hits. I'll buy the OST just for Wandering Flame (unfortunately they fukked it up in the remake). BlitzBall... lets just say I have 1000 hours put on a sidequest since I started my file when I was ten.
I highly recommend this game and think this is the objective best starting point. X2 is a different story, but after you play through a couple of FF's give it a try. It's the peak of the old ATB and Job Systems, which makes me wonder why they bothered switching.
XI MMO.
XII is overly ambitious, but it does tell the best political story. Now the biggest spite and criticisms is that the game is essentially deigned to be an offline MMO. So it follows similar systems. If you like grinding and low item drops, this is the one. Character-wise, only one of them stands out and that's Balthier.
XIII, three games so you'd assume it'd be one of the best. All I could say is, this is the equivalent of Kathleen Kennedy's Star Wars. It feels like the devs were (and later admitted) trying everything to make Lightning into the next Cloud. It failed. Lightning is unlikable, hell everyone in the game is unlikable, even the breh. The battle system is unintuitive, there are points where you could hold up and simply skip through fights. While X is linear, nobody could doubt that the world was beautiful and that everything about the game made the world seem much bigger than it actually was. This game feels restricted to corridors. There's nothing that we care about. We don't see the point in saving it. I think
XIII-2 is a better approach with better characters, but it's not enough to save it. The less said about
XIII-3, the better.
Sorry for the wall.
tl;dr- X, VII, VI, XII, XV and VII RE are decent points to start. You could go back to the others later. The last two are the latest ones and how the series is moving. If you like those, get into KH which is where they got the idea.