You can try checking out her most iconic songs~
-M
-evolution
-A Song for XX (song)
-SURREAL
-SEASONS
-Memorial address (song)
-Boys & Girls
-Dearest
-RAINBOW (song)
Those are pretty much the timless, "everyone's-favorites"-ish iconic songs ~ since they're from different times, you get to hear Ayu in very different styles, too ^^
One of the highlights of Ayu's music (the main one for me) is the lyrics though ~ so you can also just read through some lyrics, and then download the songs that you can relate to the most ^^ I think you can find all the lyrics and translations at AHS...
Divine Ayu is another good option ^^
Album-wise, I'm not sure what to recommend, since they're different, so they'll appeal differently to you depending on your taste~ I think I can describe them a bit like this:
A Song for XX - it's really old, and some people don't like it. At first listen I thought it was kind of dull, but after a while it grew on me, it has some really beautiful songs. I think the arrangement is kinda simple, but the melodies are really good~
LOVEppears - poppish dance-ish. Also kinda old, but some people seriously love this album. Great ballads~ kanariya is a REALLY WEIRD song haha XD
Duty - my favorite. I don't know, there's something so artistic about this album XD Both the music and the lyrics have a style that I don't think appears in any other Ayu albums. Like, not even a tiny bit lol. IMO it's a masterpiece, but I'm biased lol XD
I am... - has the most iconic songs in it. It has a techno-ish sound mixed with pop-rock I think... (though I'm not really good at classifying music lol). The lyrics here are also very unique. Pretty much every song is amazing... (except maybe "still alone" haha XD)
RAINBOW - pop-rock ish, I think...it's a weird album, with weird songs. But really good. There's a
thread about it that should give you a lot of information about the style and stuff ^^
Memorial address - HANABI ~episode II~ and forgiveness are both very unique songs, which are a bit love-or-hate ish. ANGEL'S SONG is a happy poppish song, ourselves and Because of you are darker rock-ish songs, No way to say is a really great ballad, Memorial address is a sad rock-ish song, and Greatful days is a summer-ish poppish song. IMO the whole album is great, except Greatful days >____<
MY STORY - really rock-ish album. It has freaking amazing songs, but with the HUGE amount of
17 tracks, I think some of them sound a bit filler-ish. About You, Moments and INSPIRE are awesome IMO~ CAROLS is also a fan favorite, many people really love this song. (I think it's because the lyrics are easy to relate to)
(miss)understood - It's a mix of styles... Bold & Delicious and Ladies Night are
weird pop songs, STEP you/fairyland/Beautiful day are happy-ish poppish songs, is this LOVE? and (miss)understood are more "violent" sounding (lol XD) rock songs, alterna and in In the corner are pop-rock ish, criminal is a power ballad, rainy day is a pop ballad, Will sounds a bit influenced by traditional japanese music...
Secret - most songs are rock(ish?) with some techno-ish elements... with some excpetions: Born to be... is a beautiful song in a different style, with a gospel choir haha XD JEWEL is a piano ballad, momentum is another really beautiful ballad, Beautiful Fighters and Blue bird are happy pop songs, kiss o' kill and Secret have this really unique style which I don't know how to describe haha XD
GUILTY - I think this is the most rock-ish album Ayu has released so far... it has great rock tracks and awesome power ballads, but also 2 pop songs (MY ALL and glitter) and a soothing, calm ballad (untitled ~for her~)
...ok. that's all. XD