In that list I'd probably start with the pillars and pendulums. The dimshields and lightnings get 1 quanta cheaper, but in terms of just this deck, upgrading a pillar or pendulum will essentially give you the same benefit, but for any card. Thus, those would be amongst my LAST upgrades in this deck. Also, some false gods have those cards. Gemini, notably, is one of the easiest false gods to beat and has lots of dimshields that you can potentially win. Eternal Phoenix has lightning, but is much harder to beat, and doesn't have very many copies. The very last card I would upgrade is the lobotomizer, because you can win Electrocutor in spins from gold or platinum arena, as well as Gemini and Decay, both of which are quite easy to beat.
Immortals and phase dragons get stronger attack, but also cost more when upgraded. Phase dragons are also winnable from several false gods. (Scorpio, Gemini) and I think Gemini might have one immortal. These would be higher priority upgrades than dimshield or lightning, but in this deck, a lower priority than your pillars and pendulums.