Between model comparison or model screening , I believe that Model Screening is what you need. Because Model Comparison requires you to build models first and generate prediction columns from those models. It sounds like that you don't know any specific models that you favor yet. Then Model Screening provides you a list of popular predictive models.
You can enter multiple Y's as you see. In general, your decision still needs to be made for one response at a time. The software is designed to help you to find the best model for every Y. If your overall criteria is different from "finding best model for individual Y", then you need to elaborate.