Hi @gemmahodgson : The default parameterisation in Fit Model is the "set the sum of the coefficients to zero so you get a coefficient for each level of the variable" as you describe. But, it doesn't show one of them (it is the negative sum of the others). You can see them all if you choose to "expanded estimates" in the pull down menu of opitons (red triange at top).
What you describe as the "last level of the coefficient is chosen as the reference" is the "indicator parameterisation estimates" option. And for up through v18 there is no option to choose the reference level. I can't speak for v19.