Netsurf requires a Retargetable Graphics Card, only in 16bit mode, which means it won't run in AGA.
I have been using iCab to browse some CSS sites on my 030 A1200, and with CSS enabled it's certainly slow at transforming the pages after they have loaded, CSS seems to be a very bulky addition to HTML designed for a world with much faster CPUs.
Still, it's pretty good that Mac OS and games run so well on the A1200 through ShapeShifter. I have talked to a few people about my experiences, and many people seem to only remember trying ShapeShifter with either the built-in video drivers (extremely slow) or other older ones from Aminet which aren't much faster. When I first installed it, I saw how slow it was... moving the mouse pointer around on screen was like a slideshow! But then I installed a replacement for PrepareEmul and a much newer video driver (both written by Thomas) and WOW! I have what feels like a full speed 030 Mac. Sure it won't play games as smooth as it would if you had a real Chunky mode (like with a RTG card or Grafitti) but it's actually usable!
Does anyone remember the game Links on the Amiga? It's a golf game that runs in 4,096 colours on classic Amigas. Well Links Pro is a newer and nicer looking version of the game, but it never came out for Amigas. But it plays like a dream on my 030 A1200 in 640x480 in 256 colours!
Sorry for rambling, but I don't think I'll EVER run out of stuff to play and muck around with on my Amigas. If anyone else wants to try, I'm very willing to help out since I've just gone through all of the setting up myself.