Every set can be ... ordered?

["MoeBlee"]

For Z or ZF, "every set can be well ordered" is equivalent to the axiom
of choice.

But what about "every set can be totally ordered"? Is it a theorem of Z
or a theorem of ZF (if so, what is the proof?) or is it independent of
Z and independent of ZF (and who proved it such?).

And what about "every set can be partially ordered"?

MoeBlee