We've already implemented an extended star network with a central server but we were wondering how we can improve it.
I'm inclined to say that your current physical network topology should reflect at least the following four things:
There's no right or wrong answers, or list of "must buy" equipment, as I'm sure you already know, just questions you need to ask yourself to help with the design you're working towards.
I've recently done a lot of design and build work on the network for my college's new campus... we spent about £500,000 on networking, all told, which gave us Cat6 connections from each classroom to the 'local' cabinet, and a backbone with multiple redundant 10Gbe links from each local cabinet to the core, each local cabinet to its 'neighbours' and a 10Gbe connection directly into this backbone for most of our servers (the ones that would benefit). In terms of your comment about star vs. tree topology, we've essentially gone for a 'wheel' topology, i.e. a star topology with links between the spokes too.
That was appropriate for us... it will be overkill for some and small potatoes for others, but mine and my bosses answers to those 4 questions were a big help in designing our network.
If you have a small network, it is acceptable to have all the machines in one subnet.
When your network starts to grow, you have to consider implementing several subnets. Otherwise, your network will be harder to manage and the overall performance will degrade gradually.
For example, each subnet can be used by a different department/section. Then, these subnets can be interconnected using a router or layer-3 switch.
Larger networks can be composed of multiple layers of connectivity to provide better performance and manageability.