And the winner is Rasperry Pi

http://www.raspberrypi.org/

I have choosen my hardware platform:

The Toshiba Libretto is to big to fit in a standard Teapot, and I don't want to unmount it.

TP-Link router are sold around 35-40$ on chineses websites, but the delivery delay may be long, and the platform looks less powerfull.

I have found some Raspberry Pi to sell in France on Ebay at 36,5€ (+3,5€ Delivery cost)... so it will be my hardware platform. It can run Linux easily, so it is an perfect base for a small web server. I saw many project far more ambitious that mine on the very active official Raspberry Pi forum. I think it will be easy to find help and documentation.

I hope receiving it next week.