We describe a survey of ancient solar-type stars down to main-sequence effective temperatures T-eff >= 5300K and within 42 pc of the Sun. The underlying Gaia-based, volume-complete parent sample consists of 1633 sources, dominated by Population I. The design of the survey is such that around 130 sources are expected to be members of Population II (tau >= 12 Gyr) and the intermediate disc (tau similar or equal to 10 Gyr). Upon completion of the search and the analyses, this sample of ancient solar-type stars will represent an increase by a factor of 4 compared to our former 25 pc survey (N = 31) and will serve as an unbiased reference to address most relevant questions on the star formation, the stellar multiplicities, and the chemical enrichment in the early Milky Way. With the first major set of analyses presented in this work, we in effect double the number of ancient disc stars now at hand (N = 60). We discuss a number of aspects on known or new companion candidates, on barium enrichment and blue straggler stars, and on a magnesium-rich and massive Population II, and we present further evidence for substructure among the local Population II stars, as formerly suspected with the 25 pc survey. In an appendix, we describe a priori survey candidates, whose analyses dismiss them as Population I stars.