Choosing the right data mining method to find the effect of each parameter over the target
You can try Bayesian belief networks (BBNs). BBNs can easily handle categorical variables and give you the picture of the multivariable interactions. Furthermore, you may use sensitivity analysis to observe how each variable influences your class variable. 

Once you learn the structure of the BBN, you can identify the Markov blanket of the class variable. The variables in the Markov blanket of the class variable is a subset of all the variables, and you may use optimization techniques to see which combination of values in this Markov blanket maximizes your class prediction.