Unless you have a RTG card then I really wouldn't bother.
I can surf the net on my A4000 fine using iBrowse, but I have a Radeon card, buckets of RAM, 68040 and a USB ethernet adapter. I shudder to think what a 68030 with 10MB and ECS would be like.
I don't know... having my computer connected to a network is more that just the WWW.
On my A1200 have do have buttons on my iBrowse configured to go to just a few friendly pages (like aminet and the portal Karlos made) but I don't really browse on it.
I'm always using the network though... FTP, SAMBA, IRC, ETC.
I would love to have ethernet on my Minimig 1.1 but i'm stuck with bluetooth serial.
For that 2000 I would look for a Denab and and you could then use a USB network board, and USB it totally useful in other ways. Another good option would be an Xsurf and it comes with a clockport so you could later add a subway. The Denab is the best bet but its made out of unobtainium.
I did have 2000, but I had a hydra board. It lacked RJ45 but you could use a AUI adapter. I set the board for "cheapernet" and connected it via coax to a old cheapo 10mb hub that had a coax port. It still was able transfer around on FTP 400K/sec as I recall.
Good luck getting the 2000 online! You can also try amibay.com. I never purchased anything from there but I like how have it set up to avoid hardware scalpers or whatever like they have on ebay. Make sure you read all their rules...