As far as classic Amigas go - Web browsing will be extemely limited no matter what you do. Lets face it - you'll need either an AGA machine, or a graphics card just to look at a page with any kind of graphics. You'll need acceleration to use the web for anything short of an experience akin to pulling hangnails.
Then there's speed - I remember trying to use Netscape in the 90's with a 386, and later a 486.. and the experience was anything but zippy. Netscape itself didn't get that much better over time either - it became bloatware in the extreme.
Netscape/Mozilla to Linux was an advent I actually watched and followed - again, on computers of the time made me think that browsing on Linux was going to be a pie in the sky too.. It wasn't so much Opera, Konquerer, Mozilla, etc got better (though they did) - it's more the machines got faster.
Something that isn't going to happen with classic Amigas right now.
For giggles load up UAE and Ibrowse if you have it - and go through various settings in an attempt to view this website... you'll see what I mean.
Which brings us to browser choices.
Unless I can be shown otherwise - Amizilla is a dead dead dead project... I remember reading up with excitement when it was suggested - I remember getting tinglies when I saw it had it's own website.. it even had it's own Eric Schwartz mascot (which is like a AmiCommunity stamp of approval). The last news I can find is August 2006 - and nothing I can download, test, look at. Even if I did - I'd be using what, something ported from 2003 source? Hardly 'up an date' browser - fails on all fronts really...
AWeb on the other hand had a software update January 2008.
Browsing their site (which I might add is easier than the hodge-podge of websearching on Amizilla) I see how they want a 'classic' browser experience AND a modern one... Seems they realize the realities and are trying to address them - the project still has activity, it has something I can download and USE... It's not as ambitious and sexy as porting mozilla, but I've seen a million and one sexi sounding open source projects with an empty CVS too.
If I were more proficient in system and network programming - I certainly know where my time and effort (were I looking to get into a browser project) would go... As it is, reading this thread and looking over the options - I know where my support will go.
I'm not trying to yank anyones chain - I'm just trying to look at it realistically.