So the great thing about Final Fantasy is that the series is widely available and easily accessible because the games are not linked (Besides obvious sequels like X - 2 or spin offs). This means that the games have multiple good entry points and no prior knowledge of any of the other games is required.
Now I do recommend the following:
Skip the NES and SNES games for now, this includes the pixel remasters. These games just "feel" very old and haven't necessarily aged all that well. Out of the SNES games, Only VI is really worth playing. If you do enjoy the series, by all means go back to them but they're not the best entry point.
Now for which one you should start with, I recommend the following: Final Fantasy VII, Final Fantasy IX and Final Fantasy X HD.
These games have some of the best world building in the series, have traditional FF gameplay and are widely available. Games released after X are much more experimental and different. They are worth playing, but if you're looking for traditional Final Fantasy, then the above 3 games are your best bet.