This is very similar to how the immersive engineering Excavator works. Each chunk has a chance of having some vein, supposedly below bedrock. The presence type and size of the vein are generated and stored per chunk, abstractly. You can find this information with a core sample drill.
Once you find a vein you like, you place an Excavator and let it "mine" the vein in that chunk.
That's a good point - I definitely don't want to just copy IE's functionality. Any thoughts on how I could make it more original?
EDIT: Hmm, what if the Mining Machine gave you a generic ore slurry that gave different things depending on how you process it?