FileMaker can be used for this purpose. "about 10 macs" is something you will need to look at very carefully as you research product data and system requirements from other pages here on the FileMaker site.
If you install FileMaker Pro on the server, you can open the database and then each user with their own installed copy (must have correct licensing) of Filemaker Pro can access the hosted database--up to 9 Simultaneous users. See how that puts you real close to a limit that may prevent this from working for you? If you install FileMaker server on the server and use it to host the database, you can support many times this number of users and gain other benefits from using a much more robust (and expensive) application to host it. Whether you use FileMaker Pro or FileMaker server to host your database, you can set up a table in the database where each record uses a container field to store a reference to the image files stored on the server. You'll be able to view the image from FileMaker as well as open the image file in the client computers default application for the image file's file type.
You can use additional fields and tables in this database to manage tags, descriptions etc so that you can search out images linked to a specific tag record and/or sort them by categories. But keep in mind that this won't happen out of the box. FileMaker is a solution design tool. You use it to create the database to the specifications you need for your business, purchase a FileMaker solution from a third party developer or you hire a FileMaker consultant to create the solution for you.
What would you need.
1) down load a free 30 day trial of FileMaker Pro and experiment with it to see if you can get it to work for you as a single user model of what you need.
2) research system requirements and product specs to determine if you want to host the files with Server and whether or not you need server advanced to host your system. If you decide to acquire a copy of Server, research the system requirements for it to make sure it will run on your server.
3) If you decide to create your own solution, spend the extra $$ to get at least one copy of Filemaker Pro Advanced. This is a "developers" copy of Filemaker pro and comes with additional tools that can save hours and hours of effort when you need to debug a script and also provides additional options for how you can design layouts to make them more user friendly. Do not buy this product just to host the database or to use as a client of the hosted database--it offers no advantages over the less expensive FileMaker Pro for those uses.
4) If you decide to create your own solution, be prepared to spend time and $$ learning more about how to use this product. There are books and training tutorials (and trainers) that can help you learn more. (and we'll be glad to answer questions as you encounter them here in this forum.)