I know from experience that the cheap, acidic paper that was used from the mid-19th to mid-20th century ages quite poorly. I would assume that engraved marble would be very durable, with (baked) clay tablets perhaps second. (I welcome correction on any of this.)
What about other materials? Papyrus? Birch bark, like the Novgorod letters? Bamboo, like the Guodian strips? Parchment / Velum? Linen rag paper? Does it vary much by condition? Would parchment survive in some conditions where linen rag paper would be destroyed, but other conditions would ruin parchment while preserving paper?
It depends less on the material and more on the conditions that preserve them. Inorganic matter, like stone and clay, are not prone to rot or mould, and even erosion from the elements takes time.
Organic matter can be observed in a variety of situations, but the key is a lack of bacteria that will prevent decomposition. This can mean hot and dry, cold and dry, cold and wet...
The Dead Sea Scrolls are parchment and papyrus, and survived inside jars - they weren't airtight, but in their location they were very dry, which prevented mould or rot forming moisture, and protected from wind or animals. The Vindolanda tablets, by contrast, survived because they were waterlogged. Made of very thin wooden tablets, they were made to folded in half after being written on. Their environment, while sodden, was anaerobic, which prevented the presence of the bacteria that would have started decomposition.
In Herculaneum (Pompeii’s equally unfortunate neighbour), the Villa of the Papyri shows us that destruction isn’t naturally the end; the papyrus scrolls were carbonised at high temperature very quickly. Bizarrely, this means they survive in a extremely fragile yet potentially readable form. Which leads me to the means by which they can be read...
Just because something looks like the writing has been lost doesn’t mean that it’s gone forever; the Vindolanda tablets had to be photographed in infra-red for the writing to show up perfectly; this is common technique for discovering more about a document in another way it might survive: palimpsest.
Many vellum and early parchment is an surprisingly durable material, a layer of writing can be scraped off and the piece re-used (this is because historically parchment is not made from paper, but animal skin). The resulting document is called a palimpsest. The most famous example I can think of is the Archimedes Palimpsest, where the original text was 10th century, a text on Archimedes, which was then re-used in the 13th century with a Christian text. There are numerous examples of texts surviving this way, often medieval and religious in nature. The original text can be read using spectrum photography and x-rays.
Parchment and vellum, made form animal skin, need dry conditions to survive. They are vunerable to moisture, and can degrade under these conditions - this is because they are made from animal skin which isn't tanned, only limed. They were exensive to produce, hence their repeated re-use over time and their protection throughout time as high value objects. Paper, papyrus and wood tablets need anaerobic conditions, which can be wet or dry.