Was a huge Final Fantasy fan back in the day. As has been said they're not linked games beyond similar running themes (Chocobos, crystals, airships, Moogles etc) unless they're specific sequels like FF10-2 and FF13-2-3.
I'd go with this order if you really want to play.
FF7 > FF9 > FF10 > FF8 > FF12 > FF15 > FF13 (also there's FF Tactics + FF6 but I don't think they're on PC.)
If you're interested in old JRPGs beyond Final Fantasy then check out these:
Xenogears, Breath of Fire 3+4, Suikoden 2+3+5, Shadow Hearts 1+2, Arc the Lad: Twilight of the Spirits, Chrono Trigger/Cross.
This is pretty much my childhood in games
![Big Grin :D :D](/styles/default/xenforo/vbSmilies/Normal/biggrin.gif)
There are other great JRPGs but those above are pretty much my favourites. I'm currently playing through Dragon Quest XI which is like a call-back to the good old days of JRPGs.