In case you didn't notice, that's on nightmare. I maxed the weapons/gear at about 13-15 minutes or so, at which point I haven't moved since.
My rough order of acquiring was to try and max missile(it feels like the best weapon), get at least a few/max unstable cores, at least 1 railgun(best bossing weapon), 1-3 nanothrusters and tractor beams, max capacitors, max shield generators, and take data amplifiers and collection fields whenever the other choices aren't those(or sometimes when they are, use best judgement). Doing this, the couple runs before tended to last to 5 minutes, and died to either bad luck(not enough firepower and/or shields) or bad play(mostly due to lasers or greed). At about that point you may need to start taking armor plating(and emergency healing) for healing more often then before, ideally don't have to take it too much before then.
Whenever you're not offered any of the above, amplifier and coolant are nice, extra nanothrusters are never bad, flak screens and (maxed)orbital shields are good(ring accelerators also ok), I like photon beam, singularity and chain lightning, pulse cannons are ok(mostly since you start with it and the first few being decent), the rest I don't like to take.
Overall, fun game.