We report on charmonium measurements [J/ψ (1S), ψ ′ (2S), and χc (1P)] in p+p collisions at √ s = 200 GeV. We find that the fraction of J/ψ coming from the feed-down decay of ψ ′ and χc in the midrapidity region (|y| < 0.35) is 9.6 ± 2.4% and 32 ± 9%, respectively. We also present the pT and rapidity dependencies of the J/ψ yield measured via dielectron decay at midrapidity (|y| < 0.35) and via dimuon decay at forward rapidity (1.2 < |y| < 2.2). The statistical precision greatly exceeds that reported in our previous publication [Phys. Rev. Lett. 98, 232002 (2007)]. The new results are compared with other experiments and discussed in the context of current charmonium production models.