This is the first paper in a series aimed at defining a statistically significant sample of QSOs in the range 15<B<18.75 and 0.3<z<2.2. The selection is carried out using direct plates obtained at the ESO and UK Schmidt Telescopes, scanned with the COSMOS facility and searched for objects with an ultraviolet excess. Follow-up spectroscopy, carried out at ESO La Silla, is used to classify each candidate. In this initial paper, we describe the scientific objectives of the survey; the selection and observing techniques used. We present the first sample of 285 QSOs (M_B_<-23) in a 153 sq.deg area, covered by the six "deep" fields, intended to obtain significant statistics down B=~18.75 with unprecedented photometric accuracy. From this database, QSO counts are determined in the magnitude range 17<B<18.75.