I normally work with design is to do it in several phases. The first one is to discover all of the requirements, constraints and drivers which then goes into a customer requirements document (CRD).
The next step is to provide a high level design (HLD).
This describes what products to use, the protocols, the logical topology, design choices, features and so on but not any actual configuration or low level details such as IP addressing, where to physically plug the cables and so on. This is instead included in the low level design (LLD) which is a very detailed document describing what ports that should be connected, all of the configuration with also a description of why something is put in there and any other details needed.
Based on the requirements we should start mapping out a topology that you think would fit the requirements.
When you have the logical topology you should decide on what devices you need to build the topology. You need to address the devices and build the configurations to setup the network to be able to reach the internet and so on. since it would depend on what level of service you decide on for the devices and how many people you expect you need to operate the network