Neither order is inherently more natural than the other as a consequence of history. English prose is written left-to-right, Arabic numbers are written right-to-left, and source code blends both traditions. It's an evergreen source of confusion.

Of the two orders, I think lsb-first is more convenient to the programmer since in lsb-first, the first bit is always index 0, consistent with how indexes work for Scheme lists and vectors. With msb-first the first index is variable, depending on the most significant bit of the integer in question. So lsb-first iteration is implicitly "anchored."