Some very underrated groups that would make my top 10 are
Concrete Blonde and The Smiths. I can make two discs of best of music with both groups. Johnette Napolitano of CB is my second favorite female vocalist after Annie Lennox, she puts her all into the music, and also plays bass (three man band). If you want an album to start off on, pick up 'Mexican Moon', an excellent album. Known songs (maybe

) by Concrete Blonde would be 'Tomorrow, Wendy', 'Joey', and 'Bloodletting'. My favorites are:
When I Was A Fool
Rain
Jesus, Forgive Me...
Mexican Moon
One Of My Kind
Someday
Walking In London
Darkening Of The Light
God Is A Bullet
Jenny I Read (favorite)
Little Wing (Jimi Hendrix cover)