They might not sound alike, but it's good to hear the music before they became New Order. Joy Division is darker than New Order. Joy Division is great and I love New Order's cover of Love Will Tear Us Apart, even though it's practically their song.
I'd start off with Joy Division - Heart and Soul. The band members in New Order were apart of that group before Ian Curtis killed himself. After getting that, get New Order - Singles. Which has all their good songs to see if you like them.
You could have fooled me with female vocals such as Dissolve Girl, Protection, Teardrop, ect. I put them on the list because the songs I have heard, have female vocals.
Massive Attack
Portishead
Old school SneakersPimps
Ladytron
Shiny Toy Guns
Sioux and the Banshees
Blondie
Stereolab
The Human League
Berlin
Fiona Apple
Bjork
Garbage
No Doubt
Tom Tom Club
Here is a dude I know. He is very talented and his music is on the Folk side.
http://profile.myspace.com/index.cfm?fuseaction=user.viewprofile&friendID=155547746