+Unfortunately, I have ended up as our de facto network administrator.+
Then you'll want to acquire a copy of DNS & BIND book (5th edition is current, when last I checked; Cricket Liu and Paul Albitz), and read it. There's a companion DNS & BIND Cookbook (Liu) available, too.
I do not know how familiar you are with IP and IP routing, but that can be another area you'll necessarily become more familiar with. There are various good books on this topic.
+Based on what you're saying, it sounds like xserve1.local.tca would work for a FQDN, and I guess I simply need a DNS that points that name to 192.168.0.184. But once I set this up and tell all the machines on our network to check the local DNS, how are names resolved for the rest of the net?+
You will want your local DNS configured as authoritative for your local network, and configured to pass along queries to other DNS servers for translations outside its purview. This is how DNS works. How to set this up for your particular case is, well, fodder for a book.
+I'll have to see how much of this I can figure out on my own, I think they're unlikely to pay for a consultant. Luckily our network is very small and will stay so, so nothing complicated is needed.+
A good DNS consultant can get your baseline network established and running correctly in a couple of hours time, and can keep the holes plugged.
From a business perspective, investing in a consultant can save you time and effort and aggravation. From your own personal and career perspective, learning DNS can be a boon. (If you're interested in getting deeper into topics such as DNS and BIND, of course.)
You might get your ISP to provide DNS translations for you. Some will, and some will charge a fee for this. This approach is the least disruptive of your time and effort, and entirely suitable for small and infrequently-changing networks.
Start with Liu's book, if you're going to roll your own DNS experience.
I'll mention the brute-force approach -- and I stress the brute-force usage here -- can involve editing and adding entries into the local hosts file. Each host in your has an entry for each node, and each node has its own copy of the hosts file. For a simple and static network, this might be sufficient. On most Unix and Mac OS X boxes, this file is the /etc/hosts file. Windows has an analog, but I don't remember the exact path. On OpenVMS with TCP/IP Services, use the verb UCX and its command SET HOST to establish the host name and address mapping. Most (all?) other systems have some analog. If/when you scale your local network upwards or if you make frequent changes, this hosts file approach will quickly become unmanageable.