The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims to find sdBs with compact companions like massive white dwarfs, neutron stars or black holes. Here we provide classifications, atmospheric parameters and a complete radial velocity (RV) catalogue containing 1914 single measurements for an sample of 177 hot subluminous stars discovered based on SDSS DR7. 110 stars show significant RV variability, while 67 qualify as candidates. We constrain the fraction of close massive compact companions {of hydrogen-rich hot subdwarfs} in our sample to be smaller than $∼1.3\%$, which is already close to the theoretical predictions. However, the sample might still contain such binaries with longer periods exceeding $∼8\,{\rm d}$. We detect a mismatch between the $Δ RV_{\rm max}$-distribution of the sdB and the more evolved sdOB and sdO stars, which challenges our understanding of their evolutionary connection. Furthermore, irregular RV variations of unknown origin with amplitudes of up to $∼180\,{\rm km\,s^{-1}}$ on timescales of years, days and even hours have been detected in some He-sdO stars. They might be connected to irregular photometric variations in some cases. ; Comment: 14 pages, 9 figures, A&A accepted