My A1200 uses a 3COM etherlink III card, and the aforementioned drivers that clemenza was talking about with Miami. (Not Miami Deluxe, though. I'm sure it would work, however) For browsers, my favorite is Ibrowse2.4, but it IS shareware, and has alot of nice features that I'm sure I couldn't live without removed. Aweb I believe is now an opensource thing, and works (though slowly) on AGA.The 3com card has a special cable for it, that ends in a regular ethernet connection (The fat looking phone plug, if your in the US. Not sure what European phone jacks look like) If your router supports DHCP, that would be your easiest bet. YAM2.5 should work fine for E-Mail, too. The biggest prob I have browsing on the 1200 is chip mem, as I run an 800x600 resolution on 2mb. I use FBLIT (also available on Aminet, I believe) to relieve some of the burden, but YAM and IBrowse particularly like to eat chip mem like a kid eating french fries. (If anybody knows any other tricks to get around this until I get a tower/ mediator for my miggy, let me know!) Also, you can use it for chatting IRC and the IM services with Wookiechat (Or Amirc, grapevine, I think theres a few other irc thingies out there), and the IM clients for Amiga. Amicq, Amiga AIM, AmiMSN, etc.. I use Jabberwocky with a gateway that supports all the chat servers I use. The only problem I have is the reset for the pcmcia port, which is easily fixed with another aminet proggy. (Cardreset, I think) I have it set to an icon on my dock menu, though I don't need to use it after a cold boot. Hopefully this help.
EDIT: I don't know where you can find one of these cards online, I guess you can get lucky on the bay once in awhile. I've seen them in Thrift shops, even.