Rainbow is my favorite Ayu Album by far! I love every single song, the music composition was wonderful, the songs were varied and interesting!

I love all of her albums, but I dont think Loveppears is as good. I have to listen to a song for like 30 seconds before I can distinguish it from any other song on the album, too many similar songs.

The other two are, or course, just compilation albums. I would recomend Ballads over best because of the remixed/re-recorded nature of the songs. if you buy best before you buy Loveppears, then when/if you do buy Loveppears, it will feel like a tremendous waste of money because you already own a majority of the songs from it.

I'm assuming that you own A Song for XX and Duty? Since you listed a list of albums you don't have. If you own those two albums then really it doesn't pay to get A Best. Since you have a majority of the songs on it except for a few. If anything I'd say:

Rainbow and A Ballads.

BUT if you don't own A Song For XX and or Duty then get A Best in place of A Ballads since with A Best you have a pretty solid collection of pre-rainbow hits.