Probably best to get a known compaible PCMCIA card from an Amiga dealer. Some used to come with TCP/IP stack and drivers IIRC - not sure if they still do that. Note that as well as cnet.device, there is a 3c589.device on Aminet which works well for 3Com 10Mbps PCMCIA Ethernet cards (model numbers containing "589", eg Etherlink III)
Serial connection: there is a NullTCP driver on Aminet that you can use with a null-modem cable, but believe me this sort of communication is painfully slow.
Chris
