  In this paper we introduce a common framework for describing the topological
part of the Baum-Connes conjecture for a wide class of groups. We compute the
Bredon homology for groups with aspherical presentation, one-relator quotients
of products of locally indicable groups, extensions of $\mathbb{Z}^n$ by cyclic
groups, and fuchsian groups. We take advantage of the torsion structure of
these groups to use appropriate models of the universal space for proper
actions which allow us, in turn, to extend some technology defined by Mislin in
the case of one-relator groups.
