Talk Normal (the 2-disc anthology) is a good starting point & overview. Welcome back, bull_in_the_leather (Urvann).
Laurie is not gay, but she's no homophobe & has many gay friends; Avant-garde as a genre is often stereotypically associated with homosexuality though.
On a somewhat related note, Laurie Anderson & Lou Reed have been a couple since 1992.
At google video you can purchase a copy of Lou & Laurie on Charlie Rose in 2002 for the
NYC Man remastered compilation & Laurie on the Charlie Rose Show from 2003 discussing her "The End of The Moon" performance piece. Each of these full programs costs only .99 cents. If your system does not meet the minimum system requirements for the stream then you will need to rename the .gvi file to .avi & play it in a media player for best results. These are excellent programs.
http://video.google.com/videosearch?q=laurie+anderson
Ubuweb has the 1981 Giorno Poetry Systems release,
You're the Guy I want to Share My Money With in its entirety for legal mp3 download.
http://www.ubu.com/sound/guy.html
of related interest is
the GPS 1985
Big Ego compilation
http://www.ubu.com/sound/big_ego.html,
A Diamond Hidden In The Mouth Of A Corpse release (1985) (no Laurie, but WSB is on it) & The Nova Convention (1978) (This is where Laurie first met & became friends with Bill) http://www.ubu.com/sound/diamond.html