I love Quo but mostly it's the "critical" 1971-1976 timeline before they went "commercial".
Lots of great tunes like Backwater, Rain, Mystery Song, Caroline (now there's a memorable song), Down Down, Big Fat Mama etc.
"Whatever You Want" must be one of their biggest hits and should be familiar across the pond too, no? Not to mention the Bolland-Bolland cover "In The Army Now".
Blues based boogie mostly but with their unique style. I think it was Lancaster who said that their lead guitarist Francis Rossi didn't really know his scales so they really avoided the cliches and came up with a sound of their own.
Lancaster had a gritty and more macho singing style but it was mainly Rossi and also the 2nd guitarist Rick Parfitt who handled the lead vocals and their poppy sound gave also a unique bent.