We describe two ground-based observing campaigns aimed at building a grid of approximately 200 spectrophotometric standard stars (SPSS), with an internal =~1% precision and tied to Vega within =~3%, for the absolute flux calibration of data gathered by Gaia, the European Space Agency (ESA) astrometric mission. The criteria for the selection and a list of candidates are presented, together with a description of the survey strategy and the adopted data analysis methods. We also discuss a short list of notable rejected SPSS candidates and difficult cases, based on identification problems, literature discordant data, visual companions and variability. In fact, all candidates are also monitored for constancy (within +/-5mmag, approximately). In particular, we report on a CALSPEC standard, 1740346, that we found to be a {delta} Scuti variable during our short-term monitoring (1-2h) campaign.