Unpolarized cross sections and double-helicity asymmetries of single-inclusive positive and negative charged hadrons at midrapidity from p+p collisions at sqrt(s)=62.4 GeV are presented. The PHENIX measurements for 1.0 < p_T < 4.5 GeV/c are consistent with perturbative QCD calculations at next-to-leading order in the strong coupling constant, alpha_s. Resummed pQCD calculations including terms with next-to-leading-log accuracy, yielding reduced theoretical uncertainties, also agree with the data. The double-helicity asymmetry, sensitive at leading order to the gluon polarization in a momentum-fraction range of 0.05 ~< x_gluon ~< 0.2, is consistent with recent global parameterizations disfavoring large gluon polarization.