What to pick for "localhost.localdomain"?

[B Wooster]

Having run Linux for years now, with multiple machines behind a
broadband router, I still am totally unclear on the concept of what to
pick for "localhost" and "localdomain" when installing a new box.

So, I added a new box to my home network of computers.

Using Fedora FC5.

At this point in time, all my home computers connect to a router,
which connects to a cable broadband provider. But I move pretty
regularly, so I don't want to use "cablecompany.com" as the domain
(and that may not be right anyway).

How do I set up my multiple computers and their hostnames?
Some computers have static IP address (for running servers), some use DHCP.

Any tips?

Just invent a domain?

"mydomain"

And then use:

"host1", "host2", etc for my home computers?