This was my exact dilema, having only played FF8, FF9, FF10 and parts of FF13.
I wasn't familiar with either song in the demo yet absolutely loved it, which for me was enough to place a pre-order straight away. My main issue with the game was that I wouldn't be familiar with and therefore appreciate huge chunks of the track list, but the demo showed me that wasn't an issue.
It's funny as I'm almost the opposite of you guys who have only played the newer games. I've played all of the NES/SNES ones and about half of IX and X but really kept away from the newer ones as they just don't compare to the old school ones.
I actually cringe whenever I hear one winged angel, so I'm just going to stay away from the newer music in Theatrythm and enjoy the older stuff =)