Cheapest way to get around the Midwest?
The cheapest choice depends a lot on when you book. MegaBus has some cheap tickets on every route, but as these go, they become more expensive. Greyhound's prices tend to be more static. It would be really rare for Amtrak to be cheaper, but it is possible its location would be better, depending on the city.
As for accommodation, if you are prepared to be flexible, Priceline will likely work well. Figure out if there is public transit from the drop off point, and then take a careful look at the zones. Also look at betterbidding.com.