Instead of just bashing your choices, allow me to show that I can also be constructive 
Throw in a little Heather Nova. That woman can SING. “London Rain” is a beauty, IMHO.
Looking through the CDs I have on hand:
Fiona Apple
Sarah McLachlan (may I suggest “Black” on Solace?)
Shirley Manson - though maybe Garbage doesn’t really fit the mood
Poe (“Dolphin” is my favorite)
Tori Amos
Natalie Imbruglia - though for “torn” I’d suggest the original author’s version: Ednaswap or Annetenna
Sneaker Pimps (I’ve forgotten the singer’s name, and she’s not a solo act anyway)
Beth Gibbons (of Portishead)
Liz Phair
Liesje Sadonius (of Hooverphonic. Again, not a solo act)
Mary Fahl (of October Project. If you don’t know her, find “Bury my Lovely”)
Erika Amato (of Velvet Chain. may I suggest “Don’t leave a Diva” for a strong women theme, or “Treason” for a really really good song)
Esthero - “Heaven Sent”
Beth Orton - “Stolen Car” absolutely rocks
Ani DiFranco.
Natalie Merchant
Rachael Sage - “Sistersong”
Before you decide, please listen to LeighAnn Hussey’s new album, Mother Night. It’s at http://www.mp3.com/nuit. Personally I prefer her ealier, more celtic-ly stuff, but this is still very good.
xtal
Janis Ian
And for something completely different, Laurie Anderson.
Aimee Mann - Wise up
Annie Lennox is another great singer who hasn’t been mentioned.
Buffy Saint-Marie - Bury my Heart at wounded knee.
check Cat power’s cover of the Stones’satisfaction.
fantastic! any of her records would do though!
PJ Harvey of course
Sarah Vaughan, Nina simone as well
Lisa Germano.
Nehna Cherry
Rickie Lee Jones
Patti Smith
Beth Gibbons of Portishead. Include tracks such as Glory Box, Roads and It’s A Fire.
Most everything else I would suggest has been covered by DoctorJ and TheNerd.
[sub]”Doctor J. and the Nerd” would make a band name . . .[/sub]
All good choices, but I’m astounded no one has mentioned Carly Simon, or Barbra Streisand.
Nicolette Larson
I would recommend checking out Sam Phillips. Brilliant songwriter, wonderful music.
Some excellent song choices would be:
Martinis and Bikinis (sounds not at all as the title may suggest.)
Power World
Strawberry Road
Animals On Wheels
Loreena McKennett
Julie Miller
Nanci Griffith
Connie Dover
Kim Richey
Kasey Chambers (just heard her today…nice)
Lucinda Williams
Dar Williams
Lucy Kaplansky
dave
Michelle Shocked
Opal (Night Train is rather haunting.)
I’m still working on it and ill be sure to post the tracklist when i get done… probably gonna be around tuesday or wednesday… but hey… itll be worth the wait! 
A few of my fav’s from my own collection:
Joni Mitchell (Just Like This Train, Morning Morgantown, Carey)
Sarah McLachlan (Do What You Have To Do, Angel)
Fiona Apple (Slow Like Honey, Pale September)
Loreena McKennitt (The Lady of Shallott, The Old Ways)
My apologies for digging up this corpse (I found it in a search on Tori Amos), but… doesn’t anybody here like Tracy Chapman??
Joan Jett and the Black Hawks ---- I Love Rock and Roll
Cyndi Lauper ---- Girls Just Wanna Have Fun
Donna Summer ---- Last Dance
another vote for Liz Phair and Aimee Mann.
Also Mary Margaret O’Hara: she only has one album that I’m aware of, Miss America, but every song on it is a classic, especially Keeping You in Mind and Body’s in Trouble.