Within the field of energy storage there are two important sub-fields... grid-level storage (cheap, long-lasting) and high-density (for transport applications). Both fields are already making good progress but I think I'd focus on grid-level first. Success here means basically being able to make the whole world's electricity grids "green". It will also be a massive economic stimulus because electricity will get very cheap.
No, you don't need "unlimited" resources for this, like I said, rapid progress is being made right now, it's just not quite rapid enough for the urgency and more focused funding and stimulus could definitely accelerate things. So if I had a lot of money and top talent I would distribute those among the handful of most promising approaches that are already being tried and keep funneling them there until it's "solved" for what we need.