An Amiga 1200, a broadband connection, a PCMCIA ethernet connection, a TCP/IP stack (Miami, AmiTCP, etc).
I don't remember offhand if the TCP/IP stacks for Amiga OS 3.1 or earlier have DHCP capability. If not then you'll probably need a static IP (unless you intend to use a Linux PC or other system for network masquerading).
If you expect it to be comparable to using a modern computer, you're going to be very disappointed. There is pretty good Amiga software for IRC and older protocols like telnet and FTP. There is acceptable software for AIM. Web browsers are pretty minimal and for the most part suck for anything but very simple all text or text with simple graphics pages.
