A thing most guys does not realize: there is a gizmo called Lantronix MSS100, which is a ethernet modem emulator.
They pop on Ebay every now and then. Wait for one for less than 30USD.
What it does? It emulates a modem using the serial port of the Amiga and translate the commands to Ethernet, so all you need is the net stack (Miami, Genesis, AmiTCP, etc), a generic Hayes modem driver and on the hardware side a router (for obvious reasons).
Here comes a link for what I said 
