PLATO (PLAnetary Transits and Oscillations of stars) is an ESA M-class satellite planned for launch by end 2026 and dedicated to the wide-field search of transiting planets around bright and nearby stars, with a strong focus on discovering habitable rocky planets hosted by solar-like stars. The choice of the fields to be pointed at is a crucial task since it has a direct impact on the scientific return of the mission. In this paper we describe and discuss the formal requirements and the key scientific prioritization criteria that have to be taken into account in the Long-duration Observation Phase (LOP) field selection, and apply a quantitative metric to guide us in this complex optimization process. We identify two provisional LOP fields, one for each hemisphere (LOPS1, LOPN1), and discuss their properties and stellar content. While additional fine-tuning shall be applied to LOP selection before the definitive choice (to be made two years before launch), we expect their position will not move by more than a few degrees with respect to what is proposed in this paper.