Pretty machine and you will LOVE that desk - so much storage! :)
When you tilt the machine back, there should be a small plate on it with one or two long numbers stamped onto it.
One number will be the serial number and the other number will begin with either 117., 148., 158., 385., or 516.
i.e. - 516.891 or 158.18033 or 148.52
The numbers before the period indicate the manufacturer (and I never can keep them straight) and the numbers after the period contain the model number.
And there's no apparent rhyme or reason to this, either - the 516.891 is a Gritzner-Kayser made machine and the model number is 89. A 516.890 is also a model 89.
A 158.18030, 158.18031, 158.18032 and 158.18033 are all model 1803's.