This paper presents measurements of W^±Z production cross sections in pp collisions at a centre-of-mass energy of 13 TeV. The data were collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider, and correspond to an integrated luminosity of 36.1fb-1. The W^±Z candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons and muons. The measured inclusive cross section in the detector fiducial region for a single leptonic decay mode is σW±Z→ℓ′νℓℓfid.=63.7±1.0(stat.)±2.3(syst.)±1.4(lumi.) fb, reproduced by the next-to-next-to-leading-order Standard Model prediction of 61.5-1.3+1.4 fb. Cross sections for W⁺Z and W^-Z production and their ratio are presented as well as differential cross sections for several kinematic observables. An analysis of angular distributions of leptons from decays of W and Z bosons is performed for the first time in pair-produced events in hadronic collisions, and integrated helicity fractions in the detector fiducial region are measured for the W and Z bosons separately. Of particular interest, the longitudinal helicity fraction of pair-produced vector bosons is also measured.