We describe the relation between spin fluctuations and superconductivity in a highly ordered sample of YBa2Cu3O6.5 using both polarized and unpolarized neutron inelastic scattering. The spin susceptibility in the superconducting phase exhibits one-dimensional incommensurate modulations at low energies, consistent with hydrodynamic stripes. With increasing energy the susceptibility curves upward to a commensurate, intense, well-defined, and asymmetric resonance at 33 meV with a precipitous high-energy cutoff. In the normal phase, which we show is gapless, the resonance remains surprisingly strong and persists clearly in Q scans and energy scans. Its similar asymmetric spectral form above T-c=59 K suggests that incoherent superconducting pairing fluctuations are present in the normal state. On cooling, the resonance and the stripe modulations grow in well above T-c below a temperature that is comparable to the pseudogap temperature where suppression occurs in local and low-momentum properties. The spectral weight that accrues to the resonance is largely acquired by transfer from suppressed low-energy fluctuations. We find the resonance to be isotropically polarized, consistent with a triplet carrying similar to2.6% of the total spectral weight of the Cu spins in the planes.