Disclaimer: I'm assuming you are installing the HDHomerun on/in the Server computer.
So, the typical setup is for the Client machines to "share" the Library and Tuner card(s) from the Server. On the Server you would go to Tools>options>Media Network and check the box "Use Media Network to share this library...", and have MC generate a sharing code/password. Then go to Client machines and under Playing Now>"Add Library", then use the code/password to link to the Server Library.
Lastly, even though you are using the Server Library you can still setup some specific viewing preference on each Client machine, such as favorite or hidden TV channels, and various views in Theater View, and such. BTW you may need to turn on the TV Feature on the clients (I don't recall whether its activated by default). You would turn it on at Tools>Options>General>Features.
EDIT: I missed you last question - when you setup the TV stuff, MC will ask you where you want to save your TV recordings. If you don't answer MC will install to it's default location (on the largest hard drive). All the recordings then go to this folder and you can then manually move those recording you want to keep to a permanent "watched" folder (after you inspect, tag, etc.) or you can leave them there and setup MC to "watch" that folder (automatically import all the new recordings into the Library). Once a file is imported the Server Library it is available to all the Clients to view.