Ed,
You are correct that your trusty 2003 server is due for replacement, for a number for reasons.
Utilizing all of the capabilities of an active domain can be daunting, but the basics are actually straightforward. It is actually very helpful to manage permissions in one location for your network.
As others have indicated, there are forms of MS servers that are more affordable for smaller businesses.
Another option is to make route entries in the domain, and map to the AC server via IP versus netBios/workgroup broadcast.
Of course if you want to save money, you can setup much the same using a Linux server, it will just take most time, which you may not want to invest.
