I understand that you have some questions about the Slingbox and how it works.
The Slingbox is a network device that will allow you to send the home TV signal to the Internet. You will be able to get the remote connection using a supported device (computer, tablet or phone). The following links will allow you to get the information about the requirements on both ends and supported devices.
first, would it be possible to setup a slingbox at family's house in st. louis, where we're from, and stream it to our tv in orlando, where we live?
Yes, since is the main goal for the Slingbox. It will allow you to get the remote connection to your supported A/V source (cable box, DVR or satellite receiver).
The following link will provide you with further details:
How does the Slingbox work?
if so, what all equipment would i need to buy and how would i go about setting it up?
our family has dish network provider as well.
The following link will allow you to get all the information about the items you need:
Finally, this link will guide you with the steps to follow in order to kno how to set up your Slingbox for Internet Viewing, no matter which Slingbox model you get since the steps are the same: