Context. Around 16% of the solar-like stars in our neighbourhood show IR-excesses due to dusty debris discs and a fraction of them are known to host planets. Determining whether these stars follow any special trend in their properties is important to understand debris disc and planet formation. Aims. We aim to determine in a homogeneous way the metallicity of a sample of stars with known debris discs and planets. We attempt to identify trends related to debris discs and planets around solar-type stars. Methods. Our analysis includes the calculation of the fundamental stellar parameters Teff, log g, microturbulent velocity, and metallicity by applying the iron ionisation equilibrium conditions to several isolated Fe i and Fe ii lines. High-resolution échelle spectra (R ~ 57 000) from 2, 3 m class telescopes are used. Our derived metallicities are compared with other results in the literature, which finally allows us to extend the stellar samples in a consistent way. Results. The metallicity distributions of the different stellar samples suggest that there is a transition toward higher metallicities from stars with neither debris discs nor planets to stars hosting giant planets. Stars with debris discs and stars with neither debris nor planets follow a similar metallicity distribution, although the distribution of the first ones might be shifted towards higher metallicities. Stars with debris discs and planets have the same metallicity behaviour as stars hosting planets, irrespective of whether the planets are low-mass or gas giants. In the case of debris discs and giant planets, the planets are usually cool, – semimajor axis larger than 0.1 AU (20 out of 22 planets), even  ≈65% have semimajor axis larger than 0.5 AU. The data also suggest that stars with debris discs and cool giant planets tend to have a low dust luminosity, and are among the less luminous debris discs known. We also find evidence of an anticorrelation between the luminosity of the dust and the planet eccentricity. Conclusions. Our data show that the presence of planets, not the debris disc, correlates with the stellar metallicity. The results confirm that core-accretion models represent suitable scenarios for debris disc and planet formation. These conclusions are based on a number of stars with discs and planets considerably larger than in previous works, in particular stars hosting low-mass planets and debris discs. Dynamical instabilities produced by eccentric giant planets could explain the suggested dust luminosity trends observed for stars with debris discs and planets.