  Superconducting resonators and parametric amplifiers are important components
in scientific systems such as kinetic inductance detector arrays,
frequency-domain multiplexers for other superconducting bolometers,
spin-ensemble based memories, and circuit quantum electrodynamics
demonstrators. In this paper, we report microwave measurements of
superconducting Ti, Nb, and NbN resonators and their use as parametric
amplifiers. These half-wave resonators were fabricated under near identical
sputtering and lithographic conditions to ensure a like-for-like comparison of
material properties. We report a wide range of properties and behaviours in
terms of transition temperatures, resistivities, rate-limiting nonlinear
response times, nonlinear dissipation, signs of the nonlinear inductances and
their dependences on temperature and resonance harmonic. We have successfully
operated Nb and NbN resonators as high gain parametric amplifiers, achieving
greater than $20\,\mathrm{dB}$ of power amplification. We have shown that for a
half-wave resonator, amplification can be realised not only in the fundamental
resonance but also in the higher harmonic resonances. Further, for materials
with high transition temperatures, e.g. Nb and NbN, amplification can be
achieved at $\sim4\,\mathrm{K}$, i.e. a temperature maintained by a pulse tube
cooler. Finally, in materials systems that have very fast response times, e.g.
NbN, we have found that a cross-harmonic type of amplification can be achieved
by placing pump tone in a different resonant mode as the signal and the idler.
This wide range of observations will have important implications on the design
and application of superconducting parametric amplifiers.
