My suggestion is to play:
FF6, FF9 and then FF7. in that order. those are the top tier games in the series. i would consider FF4, FF10, and FF5 to be tier 2. and FF8, FF13, FF1, FF2 to be tier 3. you can always go back and play the ones that are less popular, but if you dont play those 3 first, i think you would be missing out.
the main reason to play these games is for their story and characters. FF1, 2 and 3 being so old dont really do much in those respects. the gameplay is actully quite hard as well requiring some serious level grinding for very little reward. no reason to care, the characters dont have names, arnt relevant to the story in FF1, FF3 remake is not good. FF2 has the best story out of the 3, but its not worth playing through if its your first one.
FF8 is really not a good place to start. maybe some people like the "innovate" story, but the juction system is way too deep for newcomers. a lot of people got pissed with the junction system. its not a good place to start purely for this. FF13 is considered the worst game in the series by many fans and many reviewers. my opinion is avoid this game, its really not the right place to start.
FF4 and 5 are really good games, they might be worth playing through at somepoint. but for the extraordinary FF experience its not quite the right place to start. the games require some serious grinding here and there. FF10, might be worth starting here. but the remake is coming out next year, so i would wait for that. and this isnt really the right place to start because the other FF games do things so much better.
i think FF6 or 9 are a good place to start. then playing FF7 afterwards. mainly because the learning curve for the battles is relatively simple. the story picks up fast very early (FF8 and 10 take time to get interesting). and personally i find them to be the best in the series because of their characters and respective stories.
FF12 should be avoided. i actully think its a semi-excellent game, but its not a good FF to start with. the game requires serious level grinding all the time. the story and the characters are not as well developed as they shouldve been for various production related issues and the game is inconsistant.
Edit: i would recommend not looking at youtube tbh, it might spoil some things.