  Selection of the ground state of the kagom\'e-lattice $XXZ$ antiferromagnet
by quantum fluctuations is investigated by combining non-linear spin-wave and
real-space perturbation theories. The two methods unanimously favor ${\bf q}=0$
over $\sqrt{3}\times\sqrt{3}$ magnetic order in a wide range of the anisotropy
parameter $0\leq \Delta\leq 0.72$. Both approaches are also in an accord on the
magnitude of the quantum order-by-disorder effect generated by topologically
non-trivial, loop-like spin-flip processes. A tentative $S-\Delta$ phase
diagram of the model is proposed.
