Need help setting up a home LAN

[Paul E Condon <pecondon@mesanetworks.net>]

A few days ago, my old consumer grade router died, or seemed to die
such that I decided to purchase a new consumer grade router. What I
remembered about how the old router was set up was insufficient to get
me back up and running with the new router and the old LAN
configuration. I think my problem has to do with DHCP. I didn't use
DHCP in the old set up.  Instead I had statically defined IP addresses
in /etc/hosts. I can see good reasons for DHCP, but I have never
understood how I could get my four Debian hosts to talk to each other
under DHCP. I see some things that can be configured to have DHCP
assign fixed IPs to certain devices based on their MAC address, but is
that what needs to be done? What I'm looking for is the ordinary and
accepted way to make an ssh connection from one of my boxes to another
one of my boxes where DHCP is happening.

Also I used rsync to keep backups of files on two different boxes, and
approx to maintain a local Debian repository. The way I have done this
in the past is dependent on local search.

Suggestions? Useful reading material?
-- 
Paul E Condon           
pecondon@mesanetworks.net