You can't go past RAINBOW and MY STORY, they are both fantastic albums and Ayu shows of a great range of musical styles
I also recommend I am... and SECRET as well as the Ayu Trance/Ayu-mi-x albums as titles to get as you go on.
As far as PVs (music videos) go, RAINBOW (the song not the album) and Endless Sorrow are two of her best to date. You can see them on Youtube or probably get them here.
If you wanted to try out her earlier music there's a lot of her songs available for download here so you can try before you buy
I'm sure eventually you'll want all of her discography anyway, but I believe they are two good albums to begin with and are reasonably priced these days.
And welcome! Whereabouts in Oz are you? Great to see another one here!