What to put the Adventurer's Stone on:
It's up to you. I attached it to my Talisman of the Emerald Warrior because I have only one PoP flag that applies to the figurine. However, many find that attaching it to the Intricate Wooden Figurine is a good, general call.
How the Adventurer's Stone upgrades work:
-An upgrade to the stone can be gotten after every ten wins within a single dungeon theme (MMC, Tak, DGuk, Mir, Ruj).
-To get your upgrade, you must hail the appropriate NPC in the theme's corresponding camp. (This NPC is also the one who asks people the series of questions in order to obtain their Adventurer's Stone in the first place.) For example, Vual Stoutest is the NPC you would hail in the BB camp after ten wins in MMC.
-You can hail the NPC after every two wins in order to learn more of the lore about that dungeon theme, but the Adventurer's Stone will only glow and gain power after five of these bits of lore have been revealed to you within the same theme (in other words, you have to get ten wins within a single theme per upgrade).
-Eventually the NPC at the camp will tell you to go visit a different NPC (in a different zone and not at a wayfarer's camp) to learn more. Basically, the same rules apply as before. Find this NPC and hail him/her until you're caught up on lore. In the interest of time, you can wait to visit the NPC until you've hit another ten win mark within the theme (for a Stone upgrade). Just remember who it is and what zone he/she is in (if you forget the name, you can hail the original NPC in the theme's camp for a red message containing the new NPC's name).
-After you've chatted with this NPC for several rounds of lore-learning, he/she will send you back to the theme's camp to talk with the original NPC some more. This cycle continues to repeat itself as you gain more and more wins (disclaimer: my highest number of wins in any theme is currently 39, so I don't know what happens when your win count in the theme gets REALLY high).
Here's the way the stats get upgraded:
These stats will not help you unless the Adventurer's Stone is augmented onto your currently equipped charm.
Ten wins within a theme = Five bits of lore within that theme = +2 HP and +2 mana
After every fifth upgrade of HP and mana, the Stone also gets +1 to all stats and resists. When determining the + to stats, the number of HP and mana upgrades can come from multiple themes
So if I have twenty wins in Mir, ten wins in Ruj, twenty wins in Tak, and if I do all of my running around and hailing to activate the upgrades, then I will have an Adventurer's Stone that is +1 to all stats, +1 to all resists, and +10 HP and mana.
I hope that helps to clarify. :)