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Why would you choose to solve it? Do you actually need unlimited resources to start?
Aging. Nothing brings more suffering. Resource needs are considerable due to long preclinical & clinical studies necessary, perhaps also due to novel paradigms which will have to be invented along the way.
Honestly, unlimited anything is a trap: unlimited destroys. It's the limited that makes things great.
If you need unlimited, try space, or the heart of the sun.
Something, something the allegory of the Krell...
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.
poverty.
cancer.
explore ideas like UBI, modern Cybersyn, a renewed US Digital Service, various election algorithms/methods (e.g. Condorcet)
a new PARC
a new Bell Labs
Computing efficiency - The fact is that most of the transistors in a computer sit idle, waiting for their 15 nanoseconds of fame. A first principles review of what is actually possible leads me to suspect we can run LLMs and other large compute loads for 1% (or less) of the current energy requirements without new process nodes, using current fabs.
The Supply Chain - We need to have a publicly documented and tested second supply chain for everything in our society. Less efficient, and more robust ways to make every essential tool and material required for a modern society should be developed. Even if it's 1000x more expensive, it's still better to have that backup rather that being completely without options.
Radio Mesh networking - I'd set up a system in which everyone, everywhere, could stay in touch with everyone else. Governments and other organizations would handle the fiber backbone for big stuff, but a low bandwidth system that could work slowly, and globally, without it should be the thing we can all own.