My idea for different types of stones was slightly different, like we have different terrain types now there would be different areas of stones too, so some patches produce granite stones, other areas sandstone or slate. Until you buy the Geology skill all stones are the same to you and work as they do now. Once you buy Geology you can tell the difference, so the stones that were just called stone are now called Granite, etc. You also start noticing rocks for foraging, flint (in slate areas), chalk (in sandstone areas), quartz (in granite areas) and Obsidian (in mountains). Different types of stones are used for different things, statues require Sandstone and Granite for the plinth for example. Flint would make good arrows and tools, quartz as a curio and for some kind of jewlery, and chalk can be used for writing messages on blackboards, a simple construction like a drying frame with the addition of some slate. Obsidian should be really rare but have high quality.
I was covering the main categories or rock, Igneous, Sedimentary and Metamorphic, with each foragable being found in its category, if not quite geologically correct.
Edit: Underground water already exists, I've been in a cave that I needed a boat to explore.