Fish will be fine, you can put them in bags with air just like when you buy them at a fish store. They can be shipped 24-48 hrs this way if dome properly...... Depending on the number of fish and inverts it might be better to completely separate each fish from one another, I. Think it also depends on the type of fish you have.
With cycling, why not get some of the bacteria in a bottle be it dr Tim's or one of the numerous other products out there. When I purchased my fish from Florida last week, it was a completely new setup. 10+ in queen, med juv emperor and a small gold rim tang. I added some bacteria that the wholesaler let me have to try out and my ammonia has barely moved at all. I would just get some type of bacteria to kick the cycle along.... Since you are in Indy why not stop by premium aquatics, they are on the South or south east side of Indy just off the bypass.