Hello Petticoatwriter,
As meme said, your best chance for Gnomish Gold is definitely Geode Ore, and your best chance for Larkspurite is definitely Geode Rock.
But the drops are still pretty rare. For instance, I have just chopped 4 Geode Ores, the first 3 gave me 0 gold, and the 4th one gave me 2. Success rate: 2/40 chops

Besides, my last adventure to the mine gave me awesome results: 1 enchanter's essence, 1 gnomish flag, 1 firefly cage
One last cage to craft and I am done!