I’m assuming that “Starting from scratch” implies that you have nothing in the way of hardware. Asking what hardware component will need to be considered for LAN and WANs for each site requires a series of questions. Some of the questions you haven't given us the answers to include:
How much growth do you expect from the organization once the network is in place?
The backup and redundancy requirements for each site and system?
Remote users that will not be coming into the offices?
Level of technical understanding for your users?
The size, skill level and skillsets of your IT team?
Whether you need a wireless network to support users and/or guests?
In a traditional network, you will need to consider Routers, Firewalls and SPAM filtering requirements for each site. The # of Routers, Firewalls and SPAM filtering devices will depend on how each site is connected to each other (dedicated lines, VPN or other). In addition will there be a requirement for a DMZ on any of the sites?
It sounds also like the data will be centralized in several databases? Will these various databases be located centrally or distributed and mirrored across multiple sites?
Within each site you will need to know the number of users in order to predict the number of network routing devices. First create a sub netting plan to support 600 users and however many printers and other support devices will be needed. Then based on the number of nodes, the subnet strategy, will determine whether a VLAN system might be the answer or physical routing hardware.
You mentioned that two departments will need access to an Oracle server, but didn't mention if the members of those departments are distributed across all the sites or centralized in the same building where the Oracle server is located (or something in between)? Nor have you talked what user interfaces you are connecting to the Oracle data through. (Is it web based, client based and are there reporting software’s that need to talk to the oracle server?) Depending on this choice may determine the hardware devices required to support the users connection to the Oracle Database.
For each of the servers with data, there will need to be a backup system of some type that will require different levels and types of hardware depending on the distribution of the servers across the sites.
Another question about each site that you will need to ask is how redundant that site must be? If for example, all the database servers are located in one site, will they be mirrored on another site in case one site goes down? When it comes to internet connection, will each router have a fail over router in case the one router fails? Will there be redundant internet connections to each site in case of attack or failure.
We also need to talk about the reliability and speed of the connections between the various sites. If you did use Windows Active directory, normally at least one domain controller would be placed at each site to reduce logon time. If the connections between the sites were slow, it would require setting up each site as an active directory site in order to change the connection speeds. Each site might also require more than one domain controller for redundancy. A timing server or source might help reduce problems with distant site communication.
These are just some of the considerations for a traditional network site.
A simpler option might be to put all the systems in the cloud. For example,
Microsoft can host
Exchange email systems
SharePoint can be used to host all file server requirements
Dedicated database servers can be hosted on Windows Azure systems
(Don't mean to be Windows Centric, Google provides some very strong cloud server options as well.)
In these systems the vendor takes care of redundancy, backups, infrastructure support, Service level uptime, SPAM and virus software, dedicated hardware and 7X24 hour user support services. Using a cloud service can often provide much higher SLAs than a system built and maintained by the client.
In a Cloud solution, each site would then only need basic Routers, Firewalls, switches, printers, desktop level computers etc. Microsoft can even supply an agent for each desktop within the organization that would maintain patch levels and allow remote support on the device itself.
These are two extremely different strategies with very different hardware requirements. Without knowing more about the business vision and technical requirements for the organization, it's difficult to answer your question, “What hardware components do I need to build the LAN and WAN for all areas?”
You’ll be needing routers at each office that can handle being VPN endpoints so that the sties can VPN together.
Network Switches to cable everything together.
I’d recommend a couple of Windows servers running as Active Directory domain controllers for authentication. If you are going to be hosting email yourself you can look at Exchange (which you have to pay for) or some sort of POP3 services running on Linux. You will probably want to look at virtualizing most of your servers as most if not all of your machines can run within VMs. Especially your AD and email servers.