@Norway
Good choice, but the only thing you need is an ethernet card. Browsing the net with AGA and 030 is slow, but most certainly possible. Email and IRC is just as fast as it will be on PC.
My suggestion is to get the wireless ethernet card (look for a Netgear MA401 card), get it connected, and brag about your computer from 1992 that can actually browse the net at a more or less acceptable speed. Show your friends all the cool old games you have, and just enjoy it as it is.
When it comes to serious internet browsing, use your PC, since many not Amiga related sites can't be viewed correctly in an Amiga browser.