Sarah:
I suggest taking a look at the worked example in the cheese.jmp data table supplied with your JMP Sample Data Directory. The thinking and workflow for that example might be similar to what you are trying to accomplish with your problem?
Make sure to take a look at the two embedded scripts as well. The Contingency script does a nice job of showing the mosaic plots...and you'll get additional plots for your continuous variable predictors as well. The Fit Model script uses the Fit Model -> Ordinal Logistic personality to build and evaluate the model. Once you fit your model to your data, I suggest taking a look at various model fit evaluation statistics and visualizations such as the Effect Summary window, the Whole Model test, the Lack of Fit test, parameter estimates, ROC curves, confusion matrix, and the JMP Pro prediction profiler. In short there is no ONE thing to look at to decide if your model does a satisfactory job of helping you identify your 'key drivers'.
And last but not least...compare what the model is telling you to your knowledge of the process, rational human behavior, and expectations...if the model if flying in the face of process knowledge then maybe there is something amiss? For example suppose you are evaluating customer satisfaction with a telephone customer contact center and one of the predictor variables is 'wait time to talk to an agent' and the model suggests that satisfaction increases with increasing wait time...well something is fishy.
