This is not a bad game, but I suggest renting before you decide to buy it. Final Fantasy Anniversary Edition is remake of Final Fantasy: Dawn of Souls (GBA), a remake of Final Fantasy (NES), released in 1987.
The plot has received a rewrite, but the story basis is unchanged. Unfortunately, the story has become cliché and is far below today's expectations. Graphics have been remade, and they look very nice, but after 20 years, are still 2D – a full 3D remake would be a must-buy. Sound is the biggest improvement, with beautifully arranged pieces – however, they are still limited by the trite melodies expected from the NES. Lastly, an art gallery and a few extra dungeons have been added, but they're nothing to get excited over.
Unless you know what you're getting into, I strongly suggest renting the game to try it out.