The mode you play after you've finished the "main game" in the first Theatrhythm was more fun to me than the postgame from the second one, imo, so I don't think there would've been a huuuuge reason to wait unless you really wanted the extra songs, which mostly come from side games in the series. The music is still great in the first one... and I think what I love about it is even if you don't know the songs and haven't played the games they're from, they're still really easy to pick up and enjoy. I've only played a handful of FFs (uhh... I think 7, and 10-13 by the time I played Theatrhythm 1) and I still found it to be so much fun. Otherwise the main difference is just the character levelling is more fun/balanced because there are more characters to put in your party, but if you aren't familiar with them anyway, there's not as much point.
I will look into it! I have sooo many games to play but... I assume the series is like action-adventure, right? I like playing that genre in between JRPGs as a break so that sounds like the perfect. UNLESS IT'S PLATFORMING, is it platforming? I might have to just watch an LP if that's the case because I'm sooo bad at platforming and I don't want to end up hating the series due to my own incompetence LOL. ;_;