You could set up a whole Internet Café via Linux systems. Linux excels in the server/client arena.
This could be particularly attractive for a charity, as all the software would be free. Only the computers would have to be sourced and even then, could be a lower specification than their Windows equivalent.
If the power supply is unreliable, think seriously about an uninterruptible power supply for each machine. I know it will add costs, but in an unstable supply area, they will pay for themselves in a few weeks.
Clearly you will need a suitable Internet connection. I've no idea what the availability is like in Africa, particularly regarding speed. But to give you some idea, an Internet Café I visited last year in the Dominican Republic, which I am assured used a dial-up connection, managed to serve about 7 computers at a slow, but acceptable speed.
You'd need one server and however many client machines you wish to run. The server should be the higher specification machine, as it will be providing services for the rest and monitoring time spent on the machines and so on.
I'd recommend using one of the more Windows like distro's, maybe Kubuntu, which will give you all the software you need out of the box and is well supported (with paid for professional support if it's needed).
There is a software solution for charging the users, which will run on the server: click here
I would personally go for a hard wired set-up, both for security and reliability.
You'll need whatever modem is required in Africa and I'd recommend a switch (rather than a hub) for distribution to the clients.
Once it's set-up, create a backup image of all machines, and each night (day?) re-image the drive. This takes minimal time and provides a secure environment on each machine, though Linux suffers far less than Windows from potential problems in that area.
How's that for starters?