This work presents several observables for the reactions γ<italic> p</italic> → <italic>K</italic><super>+</super>Λ and γ<italic> p</italic> → <italic>K</italic><super>+</super>Σ°. In addition to measuring differential cross sections, we have made first measurements of the double polarization observables <italic>C_x</italic> and <italic> C_z</italic>. <italic>C_x</italic> and <italic>C_z</italic> characterize the transfer of polarization from the incident photon to the produced hyperons. Data were obtained at Jefferson Lab using a circularly polarized photon beam at endpoint energies of 2.4, 2.9, and 3.1 GeV. Events were detected with the CLAS spectrometer. In the Λ channel, the cross sections support the recent observation of new resonant structure at <italic>W</italic> = 1900 MeV. Studies of the invariant cross section, <math> <f> <fr><nu>d<g>s</g></nu><de>dd</de></fr></f> </math> show scaling behavior suggesting that the production mechanism becomes <italic> t</italic>-channel dominated near threshold at forward kaon angles. The double polarization observables show that the recoiling Λ is almost maximally polarized along the direction of the incident photon from mid to forward kaon angles. While Σ<super>o</super> differential cross sections are of the same magnitude as the Λ differential cross sections, there is evidence of different physics dominating the production mechanism. The Σ° invariant cross sections do not show the same <italic>t</italic>-scaling behavior present in the Λ results. …