The dissociative recombination of the lowest rotational states of H₃⁺ has been investigated at the storage ring TSR using a cryogenic 22-pole radiofrequency ion trap as injector. The H₃⁺ was cooled with buffer gas at ~15 K to the lowest rotational levels, (J, G)=(1,0) and (1,1), which belong to the ortho and para proton-spin symmetry, respectively. The rate coefficients and dissociation dynamics of H₃⁺(J, G) populations produced with normal-and para-H₂ were measured and compared to the rate and dynamics of a hot H₃⁺ beam from a Penning source. The production of cold H₃⁺ rotational populations was separately studied by rovibrational laser spectroscopy using chemical probing with argon around 55 K. First results indicate a ~20% relative increase of the para contribution when using para-H₂ as parent gas. The H₃⁺ rate coefficient observed for the para-H₂ source gas, however, is quite similar to the H₃⁺ rate for the normal-H₂ source gas. The recombination dynamics confirm that for both source gases, only small populations of rotationally excited levels are present. The distribution of 3-body fragmentation geometries displays a broad part of various triangular shapes with an enhancement of ~12% for events with symmetric near-linear configurations. No large dependences on internal state or collision energy are found.