Do any of the standard distributions come with an Objective C environment? Is there anywhere to get prebuilt Objective-C compiler and libraries? I would prefer an answer which is based on Clang/LLVM but will settle for something based on gcc.
Do any of the standard distributions come with Objective C environment?
As far as I'm aware neither Debian, Fedora, nor Arch Linux come with an Objective-C compiler, or any other related tools, by default. You will need to install them via their respective package managers.
Is there anywhere to get prebuilt Objective-C compiler and libraries?
Yes, you can download Objective-C compilers via your system's package manager. If you do not know how to install software for your system please read, "How do I install new software?".
You may be able to install prebuilt libraries from your system's package manger. If not, you will need to compile them manually by hand. You can often find the more popular, open-source libraries on Github.