I'm sorry to clarify this thread, but to connect to the Internet from an A2000 you:
1) Cannot use a Mediator.
2) Can use a modem (slowest)
3) Can use a Lantronics Serial-to-Ethernet device (slow)
4) Can use an ISDN device such as "ISDN Surfer" with the right ISDN line from phone company
5) Can use the ISDN Surfer's clock port to connect to a Subway USB device then to a USB Ethernet dongle
6) Can use a Thylacine card in reproduction mode to get another USB solution
7) Can use a Zorro II card -- A2060, A2065, Hydranet, or X-Surf

Can in theory connect a serial/parallel cable to a PC with Internet access (slow)
9) Can use a BridgeBoard plus ISA card
The two USB options are reasonably fast, but you will have a hard time finding a Subway; you can put in for a Thylacine with Genny Flick on Amibay. You find ZII cards for sale on occasion (some are reasonable in price). The Lantronics takes some help (look for Heather -- Skydiving Girl -- on Amibay) and max out at 230K transfer speed. The 10Base2 only cards are cheap, but unless you own a 10Base2 router you need a 80 buck converter plus cable, t-pieces and 50 Ohm terminators as the are all BNC connected (British Naval Connection = BNC = Coaxial cable); this solution runs the total cost toward $200. The USB solution includes other very expensive and hard to find cards: Deneb, Algor and such.
The quickest way would be to find out if your phone company has ISDN and if so, get a ISDN Surfer from Vesalia -- 65 bucks. If you want to try Lantronix or 10Base2, PM me.