I don't see any problem with playing them in release order. Are you very familiar with the series at all? If not, then you should know that every game is completely different. From the story to the world map to the characters to the battle system to the music, etc etc. There is very little that actually holds the series together, so you could literally play the series in any order you feel like. You could play 2, 6, 12, 4, 15, 3, etc if you'd like and it wouldn't matter.
However I'm still gonna recommend playing in release order. My first games were 10, 7, 10-2, 8, and 9 (in that order). I played all of the more modern games before I played the older ones, and I the played them as 1, 2, 4, (12), 3, 5, 6. Only reason I played 12 then was because it had just come out at the time. And 3 was on it's way out for DS when I played 4.
Anyway, so I practically played them in order and it was fine. 1, 3, and 5 are only vaguely similar because they all use some form of job system, and they all use the crystals as their base plot device.
If you wanna play them in release order, one thing you'll have to look forward to is the increase of quality in story telling and mechanics (for the most part). Whether or not 2 is better than 5 is really up to your own opinion, but 2 (as an example) has much more primitive battle mechanics than 5 (as an example).
tl;dr: Play them in release order, you'll be fine. And you'll only subject yourself to a fanboy war of which is better, 4 or 6? Plus if you've never played the franchise at all, you can have the special opportunity of playing them all in release order. Something I very much wish I'd had the chance to do.
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