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Almost all S550 Mustangs come either in a Base or Premium trim. If you've got the large touch screen on the center dash above the AC controls, you've got the Premium trim.
Long term update. I haven't really noticed the thump (maybe I'm too used to it), but I think what I feel is much closer to Intepred175's explanation (thanks, BTW). That is to say, I don't always experience it, or it doesn't present the same way each time. I have about 18k miles on the car.
I recently installed Steeda rear sub frame braces and the drive train thump has been eliminated. It tells me the thump comes from a pliant rubber mounted rear sub frame when engaging first gear.