In chronological order (I'd probably go mad trying to order these, save for having Liberi Fatali at the start and Holding my Thoughts in my Heart at the end):

Tifa's Theme (FFVII)
FFVII Main Theme (Arranged Version - FFVII)
Flowers Blooming in the Church (FFVII)
Holding my Thoughts in my Heart (FFVII)
Life Stream (FFVII)
Aeris' Theme (FFVII)
Liberi Fatali (FFVIII)
Fisherman's Horizon (Piano Version - FFVIII)
The Castle (FFVIII)
The Extreme (FFVIII)
Ending Theme (FFVIII)
The Place I'll Return to Someday (FFIX)
Over the Hill (FFIX)
Eiko's Theme (FFIX)
Oeilvert (FFIX)
You Are Not Alone (FFIX)
Melodies of Life (FFIX)
To Zanarkand (FFX)