Notice that politicians don't even bring up the national debt, or maintaining a budget any more. I guess that's proof enough that it is not manageable and that it is a lost cause. More Money Today!
Which one do you like better? Circulated $2.50 is under $400. I am not sure where you can buy a Proof sovereign for close to melt, but this will give an idea as to the design. Half sovereigns should priced at close to melt. They have the same design, but are half the size.
Half Sovereigns( I hate to disagree with @johnmilton but I would go with an older George V rather then a modern Proof but both are nice) or Quarter Eagles would be my picks as well. If you like Byzantine coins those would be cool as well. I would favor something history over current bullion but a 1/10 oz would be a nice way to own some gold as well (you might even be able to get a 1/10 oz bullion plus a light European gold coin as well) if you go modern factional AGE, Maple Leaf ,Krugerrand or Australians would be my picks
The only George V sovereign I have is an MS-65 which would be misleading. I bought a set six Proof half sovereigns for 6% under melt at a local show before the pandemic.