I think mainly we want to see how Transcendent Offense develops (we have hints of Red Wave / Blue Wave, or of decreasing the suicide cost of Static Wave), before deciding what proportion of our effort we want to devote to it. I do think that we should go beyond a singular levelup, as in continue to work on this ability even if we don't devote to it entirely.
Of the rest, the low-hanging fruit is Teleport Speed, we can hopefully Master that quickly. Interdiction Precision is stated to give a benefit, so there's that I suppose. I'm not too impressed by the description of Gate, but we should get it to usable levels I suppose.
I'm dubious on the utility of mastering other weapons. What I actually want is our other Heavy Particle Projectors back. Hypervelocity Cannons seem inferior in more ways than just unfamiliarity. Improving our skills with Lasers might be important, however, as speed of light precision weapons are handy for interception. Missiles... I guess it depends.