Quantum overlays will take 1 week and 1 day.
So, after I've done that what should I research?

I'd say energy - just get the next tier of relays. It's better to have too much energy than not enough.
After that, go for planets, up to +5 structures. That'll give more research, and in turn you'll get other stuff faster. Don't bother with +6s, skip to +8s.

Makes sense with the structures... I only install 1 core, so I don't need relays. Not enough energy is FTW!

EDIT: Actually, I max in research anyway due to school, so structures aren't that higher priority.

Always good times when you come home from school and have maxed out on rp

Go for hull p to Merged Nexus, then structures +8 (I upgraded my planets from +5's to +8's, and gained +700rp an hour more, from 6 planets)

Or, get the 1st tier of antimatter - just for the minefields. The guns cost unrealistic amounts at your rank - but this could be another reason to do +5 structures.

Well. Funding isn't too much of an issue... the amount in that pic is actually really low because I'd been messing about with my ship config and accidently sold my singularity launchers.

I only run 6 antimatters, and upkeep is 127M a day. If you can't produce that, don't get them. Get mining planets or better structures first.

Again, it's better to have too much than too little.

I would say AI logistics definetely!!!, at least up to Hybrid Theory

True - at your rank, it's not unrealistic to have up to AI logistics - allows contribution up to lvl4 bases. You only need the 1st tier.

I should get AI logistics done before Quantum Overlays if you haven't invested too much in it already.