What do I need for initial set up? Tranny cooler and?

Good idea to add the trans cooler. As to the Prodigy, yes that's a good controller. If you pick up the Tekonsha pigtail adapter for your Tahoe, it will be plug and play. The Tekonsha website will have the model number of the pigtail which your can pick up at any RV store or Amazon, Ebay, etc. They're under $15.