The Amiga SDK ("Software Development Kit") is geared towards AmigaDE. That's not what you want. Development kits for AmigaOS
are called "NDK" ("Native Development Kit"), the most important things in there are the includes and the autodocs (that's the API documentation you're searching for).
You can either try to by the "AmigaDev CD 1.2" (this one contains NDKs for OS versions 1.x, 2.x and 3.0/3.1 - plus a lot of other stuff). It's very old and therefore very cheap.
The AmigaDev CD 2.1 contains everything from the v1.2 CD plus the OS 3.5 NDK and the full version of StormC3, a commercial IDE/Compiler). It ships for 25 Euro (IIRC).
The NDK for AmigaOS 3.9 is available for download at http://www.amiga.com/3.9/download/
If you want the RKRMs ("ROM Kernal Reference Manuals", pretty essential if you're new to the Amiga), you'll have to buy one of the DevCDs (or do a Google search...). They cannot be freely distribued, as Addison&Wesley still somewhat own the distribution rights (I think).
But the ROM Kernal reference Manuals are pretty outdated, they're only covering AmigaOS 1.x and 2.x, they were never updated to match OS 3.0+. They will be updated for OS 4.0 again.
Developing AmigaOS applications for PPC Amigas: Forget about it until OS4 comes around. Developing WarpOS/PowerUp applications (AmigaOS3.x PPC extensions) is a PITA.