On which computer do I load the Slingbox software?
Wherever you want to watch it.
So do I install the software on their computer in Ohio, my computer in michigan or both?
Yes, the software will be necessary to configure it, and can install it on additional computers wherever you want to watch it.
Also, do I really need to have all the hardware set up before downloading the software?
Nope. Though, the Slingplayer client software is useless without the Slingbox server.