How well will this setup surf the web? What kind of web browsers are available? I figure it won't do web video (heck, my Mac PowerBook 400MHz won't do web video!) but can it do other modern web stuff like HTML 5, etc?
Using a webbrowser on a classic Amiga is, well, a rather interesting experiencen when you are used to more modern computers and browsers.
In short: browsers for the classic Amiga are completely outdated when it comes to supporting any more or less recent webstandards and even a pretty decent Amiga (68060@50 MHz with 64 MB ram, ethernet, scsi-drives) will not make it an enjoyable experience. Sites like Aminet work, albeit rather slow, and display correctly but more modern websites (CSS!) either have a completely mangled layout or (partly) refuse to work.
There's more than just browsing the web, though, and when it comes to ftp, irc, e-mail and stuff the situation is entirely different. The best programs available on the Amiga for different tasks range from pretty decent to very good in which case a decent Amiga (68020 and up, several MB of fastram) will provide you with an enjoyable experience on the internet.