The hardware requirements can be quite modest by todays standards and can often be satisfied by rejuvinating an older machine.
As a starting point, consider as a minimum:
CPU – 500 Mhz
RAM – 256MB
DISK – 20GB
The RAM should be as large as possible.
If 2 identical (or nearly identical) hard drives are available, consider using them in a RAID 1 configuration. This will protect your data in the event of a disk failure.
The server should work headlessly if possible, i.e. without a screen, keyboard or mouse.