I would say that her best album woul either be "LOVEppears" or "I Am..." Rainbow is really good, but in my opinion it only has a handful of songs that are really worth spending the money one, where as "I Am..." every song is worth your money.
"A Best" is by far my favorite Ayu album. But the difference with this, with exception to the first three tracks: "A Song For XX", "Wish" and "Depend on You", everything else are just tracks you can get on "LOVEppears" and "Duty". I love "A Best" due to it's mixture and the re-recording of "A Song For XX" which is way better then the original in my opinion.
As for suggestion if you want to break into Ayu, "I Am..." is your best bet. That CD has arguably one of her best works.