Need an Introduction to Tiny Core? Or peruse Core Concepts.
On uclibc, while there's (so far) no binary-only software on ARM to worry about, uclibc still loses in features and performance (and has a bit more bugs). On these grounds I would recommend against it.
musl lacks many features, and focuses only on standard-correct small functions.This means it occasionally breaks software that works fine on uclibc, due to some nonstandard-but-defacto usage for example.