In the book it's chemicals (gunpowder) and radios. The application of radios by Vinge's version of non-anthropomorphic intelligences is especially interesting.
What about a "Mote In God's Eye" -style technology bunker? Would having a set of raw materials, instructions, and tomes of information be the ideal setup? Perhaps something along the lines of the Svalbard Seed Vault. What are the most useful artifacts that can survive A) the catastrophe and B) the length of time it takes for the artifacts to be recovered? Such a timeframe could be short or many, many generations long (even geologic time?). Do we want this to potentially survive until the next intelligent being evolves, in the case of total destruction of mankind? What sealing mechanism would still be noticeable and breach-able by a low-tech civilization?
Or do we want to assume there is NO remaining technology and we're attempting to bootstrap from pure knowledge? Either way, I think it would be an interesting problem to solve.
I might even say that it's better to explore as much of the problem's causal underpinnings as a first pass.
As a budding design engineer, one of the things that has been hammered into me is first to understand the problem in its wider context. Oftentimes just identifying a PROBLEM as opposed to a TASK is not enough: you need to understand the system that enabled the problem to exist. What aspect of the system is directly detrimental? Why is it detrimental? What features of the system influence that detrimental aspect? Why do those features exist in the first place? Can their core function be satisfied through a different principle of operation, or by restructuring the functions and flows of the system, or even by redefining your requirements?
Only once you understand the system holistically and identify functional requirements, causal structure, and your available tools can you really begin to accurately evaluate your options.