The first is a good computer (or computers). Whether it is a laptop or a desktop, the computer is the heart of your organization.
Is your staff going to be working in the field or telecommuting? Then laptops are the way to go. If a majority of your work is done in the office then a standard desktop will suit all your needs.
Consider the size of the memory. If your organization does a lot of graphics work or needs to store a large amount of data locally you will need to invest in a computer with a large amount of memory.
If your organization has an exceptionally tight budget you can consider investing in refurbished computers. TechSoup is one source for refurbished computer equipment.
Next is a printer. Even if your organization is striving to be paperless there will always be certain items that must be printed.
Take a moment to consider exactly what you will be printing. A small desktop unit that prints both color and black and white is perfect for printing acknowledgement letters and other small print jobs, but if you are doing in house brochures or other marketing materials consider a larger unit.
It is no longer necessary to have a stand alone fax machine as most small desktop printers come equipped with scanner and fax capabilities.
Another hardware consideration is cellphones, your organization might choose to provide smartphones to your employees if they are out in the field or if they will be expected to deal with confidential information regularly via their smartphone.