3.9 and 4.1 are actually based on the real Amiga sources AFAIK.
The guy who wrote the AmigaOS 3.x API calls got upset that someone scanned his book into a PDF file and pirated it. So he didn't make an AmigaOS 4.x API calls and without knowing them it is hard to make Amiga 4.x apps.
AROS made their own Kickstart ROM for Classic Amigas to run AROS on Classic Amigas. Since AROS supports networking it is possible to rig up some sort of Internet connection and port a web browser to it.
Amiga Forever is worth it for the ROM images and Kickstart disks to run Workbench and other things.
Currently on my bookshelf.