  Photoevaporation of planet forming discs by high energy radiation from the
central star is potentially a crucial mechanism for disc evolution and it may
play an important role in the formation and evolution of planetary system. We
present here a new generation of X-ray photoevaporation models for solar-type
stars, based on a new set of hydrodynamical simulations, which account for
stellar irradiation via a new, significantly improved, parameterisation of gas
temperatures, based on detailed photoionisation and radiation transfer
calculations. This is the first of a series of papers aiming at providing a
library of models which cover the observed parameter space in stellar and disc
mass, metallicity and stellar X-ray properties. We focus here on solar-type
stars (0.7 M$_\odot$) with relatively low-mass discs (1% of the stellar mass)
and explore the dependence of the wind mass loss rates on stellar X-ray
luminosity. We model primordial discs as well as transition discs at various
stages of evolution. Our 2D hydrodynamical models are then used to derive
simple recipes for the mass loss rates that are suitable for inclusion in
one-dimensional disc evolution and/or planet formation models typically
employed for population synthesis studies. Line profiles from typical wind
diagnostics ([OI] 6300 $\overset{\lower.5em\circ}{\mathrm{A}}$ and [NeII] 12.8
$\mu$m) are also calculated for our models and found to be roughly in agreement
with previous studies. Finally, we perform a population study of transition
discs by means of one-dimensional viscous evolution models including our new
photoevaporation prescription and find that roughly a half of observed
transition discs cavities and accretion rates could be reproduced by our
models.
