This is a tough one for me. I got into them through watching the Jonathan Demme film on BBC2's Arena programme when i was about 10 years old. I videoed it on a Betamax which i then kept for years just to watch the film over and over. I played it so much that to this day my mum can sing along to most of the tracks.
I got a hold of Speaking In Tongues on vinyl recently and although the classics off Stop Making Sense dont sound as good (as noted on the sleeves of that album), i think its their best album, although as a listening experience you could argue Stop making sense is the best as the sound is so 'house music' imo. One or 2 are better in their original form though, classic example being Swamp. Swamp is the track playing in the party in Risky Business with Tom Cruise. Facto.
The american public agreed as it was their first million selling album but i agree that 77 and the name of the band are great albums too.
Burning Down The House
Making Flippy-Floppy *
Girlfriend Is Better *
Slippery People *
I Get Wild/Wild Gravity *
Swamp
Moon Rocks *
Pull Up The Roots
This Must Be The Place (Naive Melody)