Barcode- I highly recommend this as almost exactly what you want to read based on your description. It's an older book, Miller being one of the early Sci-Fi writers, and it's a quick read, too. The main focus of the book is on how language and knowledge are preserved over many centuries, long after an apocalypse, and what bits are rediscovered and misinterpreted. The story follows one individual, then leaps forward in time, several times, to other individuals. It's quite interesting both on its own and as an example of how early Sci-Fi can maintain some longevity when it focuses more on ideas than technology.
As to the rest, I think it was best mentioned above that things would get scavenged and recycled. Because of this, I think you would be safe deciding which bits you want to have survive, decide how they would, and have all other stuff picked clean if they would have otherwise made it through time intact. Imagine the earliest dwarves of your world mining away all of the remnants of the once great cities. Imagine early cults determing that plastic is evil and destoying it all in acid baths until there was nothing left and the cults dispersed some era prior to your campaign beginning. Any other pieces of technology you did not want to exist in your campaign can always have found itself disused, dismantled and destroyed (purposefully or accidentally), so choose what things you want to keep, and discard the rest (IMO)...