Hi Foogy,
Rockshed AO is the way to go as Bikerrandy mentioned above. From what I have taken in on RTH regarding polish, members do well with purchasing mostly OA polish on a majority of stone types. Seems Rockshed is the most popular on here and I have switched myself to Rockshed as well.
It is recommended that you stick with the same company/brand for purchasing all your grit steps and polish too.
I searched and found a specific stone polish list linked from Mama's Minerals that you may find useful.
Actinolite: Tin Oxide
Agate: Cerium Oxide, Tin Oxide
Alabaster: Tin Oxide
Amozonite: Tin Oxide
Amber: Tin Oxide
Amblygonite: Tin Oxide
Andalucite: Tin Oxide
Apatite: Linde A (Sapphire), Chrome Oxide
Aventurine: Tin Oxide
Azurite: Tin Oxide, Chrome Oxide
Apophyllite: Chrome Oxide
Aragonite: Chrome Oxide
Axinite: Cerium Oxide
Barite: Chrome Oxide
Benitoite: Cerium Oxide
Beryl: Cerium Oxide, Tin Oxide, Diamond
Bloodstone: Cerium Oxide, Linde A (Sapphire)
Brazilianite: Tin Oxide
Calcite: Tin Oxide, Chrome Oxide
Cassiterite: Tin Oxide
Celestite: Chrome Oxide
Cerossite: Chrome Oxide
Chrysoberyl: Diamond
Coral: Tin Oxide
Corundum: Diamond
Cubic Zirconia: Diamond
Danburite: Tin Oxide
Datolite: Tin Oxide
Diopside: Chrome Oxide
Dioptase: Cerium Oxide
Diorite: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Enstatite: Tin Oxide
Epidote: Tin Oxide
Euclase: Tin Oxide
Feldspar: Cerium Oxide, Tin Oxide
Fluorite: Tin Oxide, Chrome Oxide
Garnet: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Diamond, Chrome Oxide
Goldstone: Cerium Oxide, Tin Oxide
Hematite: Cerium Oxide
Hickoryite: Linde A (Sapphire)
Howlite: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Hypersthene: Tin Oxide
Jadeite: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Jasper: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Kyanite: Tin Oxide
Labradorite: Tin Oxide, Chrome Oxide
Lapis Lazuli: Tin Oxide, Linde A (Sapphire), Chrome Oxide
Lepidolite: Chrome Oxide
Limestone: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Malachite: Tin Oxide, Linde A (Sapphire), Chrome Oxide
Moonstone: Tin Oxide
Nephrite: Tin Oxide, Linde A (Sapphire), Chrome Oxide
Obsidian: Tin Oxide, Chrome Oxide
Onyx: Cerium Oxide, Tin Oxide, Chrome Oxide
Opal: Cerium Oxide, Tin Oxide
Peridot: Tin Oxide, Linde A (Sapphire), Diamond
Petrified Wood: Cerium Oxide, Tin Oxide, Linde A (Sapphire), Chrome Oxide
Phenacite: Tin Oxide
Pollucite: Tin Oxide
Quartz: Cerium Oxide, Tin Oxide
Rhodochrosite: Tin Oxide, Linde A (Sapphire), Chrome Oxide
Rhodonite: Cerium Oxide, Linde A (Sapphire), Chrome Oxide
Ruby: Diamond
Rutile: Linde A (Sapphire)
Sapphire: Diamond
Scapolite: Cerium Oxide
Scheelite: Chrome Oxide
Serpentine: Tin Oxide, Linde A (Sapphire), Chrome Oxide
Smithsonite: Tin Oxide
Sodalite: Cerium Oxide
Sosolite: Cerium Oxide
Spinel: Tin Oxide, Linde A (Sapphire), Diamond
Spahlerite: Chrome Oxide
Spodumene: Tin Oxide
Sunstone: Tin Oxide
Thompsonite: Cerium Oxide
Tigereye: Cerium Oxide, Tin Oxide, Linde A (Sapphire)
Titanite (sphene): Tin Oxide
Topaz: Tin Oxide, Linde A (Sapphire), Diamond
Tourmaline: Tin Oxide, Linde A (Sapphire), Diamond
Turquoise: Cerium Oxide, Tin Oxide, Linde A (Sapphire)
Unakite: Cerium Oxide
Varicite: Cerium Oxide, Tin Oxide, Linde A (Sapphire)
Vesuvianite: Cerium Oxide
Williamsite: Linde A (Sapphire)
Wonderstone: Tin Oxide, Linde A (Sapphire)
Wulfenite: Chrome Oxide
Zircon: Tin Oxide
Zoisite: Cerium Oxide
link origin
mamasminerals.com/pages/List-of-Recommended-Tumbling-Polishes-for-Selected-Rocks-%26-Minerals.html