A1200 + Hard Drive + 3COM Etherlink III PCMCIA network card (and driver) + TCP Stack (MiamiTCP) + additional ram and optionally accelerator.
FTP, IIRC, Mail, Telnet all work great. But Web browsing, as others have also said, will be painfully frustrating. My 1200 w/ '030@50Mhz and 16MB did better then I expected, and 10 years ago might have screamed. But the web is quite different now, most sites think nothing of having megabytes of pictures and ads. Not to mention animations, code, etc. With even the simplest pages sometimes using a couple hundred KB.
It was interesting to setup and I enjoyed doing it, but I wouldn't spend a lot of money doing it. Just not worth it. Good news, a lot of the hardware can be found on Ebay cheap (except the accelerator).