Dunno what to research after supernova, ideas?

i would say depends on play style and rank really. if your heavy pvp id say go for thetas / defense. if your heavy into missions id say stick with energy and get the last relay. after that I sould suggest getting +12 planet structures but only if you think you can afford them.

Do shields up to th first level of Obviators, for the Obviator Barrier structures

The, do Trans-Temporal Nacelles, Thetacron Cannons, and X-Manifold Detectors. The order in which you do them is up to you.