Disclosure: I work for a small company that provides Systems Administration for other small companies.
There are products like Labtech that allow you to install a management program on every computer, and then the management program reports back to the server with each system's details: Serial number, make, model, software installed, hardware installed, and much more. When we get to a new site, we install the management tool on a server, push it out to each device with a logon script, and pretty quickly have a very detailed overview of the local network. Each geographic location can be scanned in a similar manner, and report back to the central management server.
These types of products are probably cost-prohibitive for the size network that you described, but you may be able to find a local company to work with you to get your stuff documented. If not, there are probably similar tools that are available for a setup of your size.
The advantage of these types of tools is that they track your devices for you, and allow you to query them quickly for almost any information that you would like. You can set up alerts to tell you when a system is three years old, for example, and potentially up for replacement.
These types of tools free you up to do what is probably more important in your case: Dealing with what will make your users more productive.
Good luck! It sounds very exciting.