I sing it mostly as the Rolling Stones version although I love the phrasing of the words "Gallup New Mexico" in the Manhattan Transfer version so that is the way I sing it leaving a bigger than usual gap before the phrase. Otherwise we use something like the Keith Richard riff throughout.
This is a song we usually do late in the evening because it is a fast dance tune. It is one that everyone likes to sing along with so it serves well in the later evening.
I love about American music that they are unafraid to immortalise their geography in their popular songs. Somethings we are not so good at in Australia. Guess you can find some references in the collected works of Cold Chisel "boiled for an hour 50 miles out of Euston".
I actually noted 50 miles (80km) out of Euston last time I drove that way. Then I wondered if it was before or after that Jimmy boiled. Probably before after a long run from Hay and Balranald. I should get a photo next time I pass through. We should all post our photos 50miles out of Euston like Eagles fans like to take pictures "Standing on the corner in Winslow Arizona." I wonder what other song quotes merit a photograph.
Route 66 is American as you get. It is a rare night that we dont do this song. I sing it in A. It is the key I first tried it in. These days I could probably manage even in C if I pushed hard enough. It would make a nice segue then into Roll over Beethoven which I do do in C.