Wide-area photometric and astrometric (Gaia DR2) study of the young cluster NGC 6530

(abridged) NGC6530 is a young cluster with a complex morphology and star-formation history. We present a statistical study of its global properties using a new large list of candidate members down to masses of 0.2-0.4 Msun and Gaia DR2 astrometry. We consider a wider sky region compared to previous studies, to investigate the whole cluster and its neighborhood. We study the distribution of extinction and age across the different regions, and obtain constraints on the star-formation history. Cluster membership is determined on the basis of X-ray data, H-alpha emission, near-IR and UV excesses from VPHAS+, UKIDSS and other surveys, and Gaia DR2 astrometry; we also use a novel method for photometric selection of M-type pre-main-sequence cluster members. The list of candidates includes nearly 3700 stars, of which we estimate ~2700 genuine NGC6530 members. Using Gaia parallaxes, the cluster distance is found to be 1325 pc, with errors of 0.5% (statistical) and 8.5% (systematic), in agreement with previous determinations. The cluster morphology and boundaries are established with great confidence, from members selected using different criteria. There is no diffuse population of members around the cluster, but there are minor member subgroups (associated with the stars 7 Sgr (F2II-III) and HD 164536 (O7.5V)) in addition to the two main groups in the cluster core and in the Hourglass nebula. We find a pattern of sequential star formation, between ages of <0.5 Myr and ~5 Myr. Extinction is spatially non-uniform, with part of the population still obscured by thick dust. The precise Gaia proper motion data indicate that the NGC6530 parent cloud collided with the Galactic plane ~4 Myr ago, and we suggest that event as the trigger of the bulk of star formation in NGC6530. The internal cluster dynamics is also partially resolved by the Gaia data, indicating expansion of the main cluster population.