  We consider families of simple polytopes $P$ and simplicial complexes $K$
well-known in polytope theory and convex geometry, and show that their
moment-angle complexes have some remarkable homotopy properties which depend on
combinatorics of the underlying complexes and algebraic properties of their
Stanley--Reisner rings. We introduce infinite series of Golod and minimally
non-Golod simplicial complexes $K$ with moment-angle complexes $\mathcal Z_K$
having free integral cohomology but not homotopy equivalent to a wedge of
spheres or a connected sum of products of spheres respectively. We then prove a
criterion for a simplicial multiwedge and composition of complexes to be Golod
and minimally non-Golod and present a class of minimally non-Golod polytopal
spheres.
