I see no instructions how to build libcxxabi… There does seem to be a “buildit” inside of libcxxabi/lib, but what envvars / parameters should I feed it? For example, do I need to set the triple?
Use libcxxrt. While libc++abi is theoretically possible, it's really aimed at MacOS which has a separate libunwind, which means you would need to find and build a libunwind for Linux too.
libcxxrt is easier. Also, I recently submitted a patch that should make usage of the resulting libc++ easier. You might want to grab it (mail thread is called "Fixing common linking issues in Linux" or something like that) and apply it to your libc++ tree.
Again, I have already built Clang 3.5 successfully using GCC, so I’m wondering also if I need to build libcxxabi and/or libcxx using Clang or GCC?
You should build these things with Clang. In theory it shouldn't matter, but I recommend Clang, because you will link them with your Clang-built actual code.