  We present three-dimensional simulations of the core-collapse of massive
rotating and non-rotating progenitors performed with the general relativistic
neutrino hydrodynamics code CoCoNuT-FMT and analyse their explosion properties
and gravitational-wave signals. The progenitor models include Wolf-Rayet stars
with initial helium star masses of $39\,M_{\odot}$ and $20\,M_{\odot}$, and an
$18\,M_{\odot}$ red supergiant. The $39\,M_{\odot}$ model is a rapid rotator,
whereas the two other progenitors are non-rotating. Both Wolf-Rayet models
produce healthy neutrino-driven explosions, whereas the red supergiant model
fails to explode. By the end of the simulations, the explosion energies have
already reached $1.1\times 10^{51}\,\mathrm{erg}$ and $0.6\times
10^{51}\,\mathrm{erg}$ for the $39\,M_{\odot}$ and $20\,M_{\odot}$ model,
respectively. The explosions produce neutron stars of relatively high mass, but
with modest kicks. Due to the alignment of the bipolar explosion geometry with
the rotation axis, there is a relatively small misalignment of $30^\circ$
between the spin and the kick in the $39\,M_{\odot}$ model. In terms of
gravitational-wave signals, the massive and rapidly rotating $39\,M_{\odot}$
progenitor stands out by large gravitational-wave amplitudes that would make it
detectable out to almost 2 Mpc by the Einstein Telescope. For this model, we
find that rotation significantly changes the dependence of the characteristic
gravitational-wave frequency of the f-mode on the proto-neutron star parameters
compared to the non-rotating case. The other two progenitors have considerably
smaller detection distances, despite significant low-frequency emission in the
most sensitive frequency band of current gravitational-wave detectors due to
the standing accretion shock instability in the $18\,M_{\odot}$ model.
