I don't know if this has been done before. I made a diagram of the card Types based on the order they're listed on the card.
Action > Treasure > Attack > Knight > Victory > Reaction > Shelter
|__ Night __| |____ Duration ____||_____ Castle _____|
|____ Reserve ___| | |_____ Heirloom ____|
|________ Spirit ________|
If a Type is to the left of another, that means it always appears to the left of the other. Types on top of each other means it's unknown what their order would be. So Treasure and Night are after Action and before Attack, but their positions with respect to each other are unknown. Similarly, Duration is after Attack and before Reaction, but while it's known that Knight is before Victory, it's unknown what Duration's position is with respect to either.
There's a bunch of types we don't know much about: Ruins, Gathering, Zombie are after Action; Prize, Looter, Traveller, Fate, Doom are after Attack.
Some patterns can be discerned. Types that indicate the phase a card can be played in are always at the beginning, and they appear in the order of the phases. Types that indicate how a card functions are usually before types used more for convenience (like Spirit and Castle). There also seems to be a bit of animacy hierarchy: It's interesting to note that Knight is before Victory and Castle is after, even though they're both types of convenience referring to mixed piles. Knight apparently comes before Victory simply because it implies something alive.
Cards with unique dual-types:
Crown: Action > Treasure
Werewolf: Action > Night
Coin of the Realm: Treasure > Reserve
Fool's Gold: Treasure > Reaction
Idol: Treasure > Fate, Attack > Fate
Diadem: Treasure > Prize
Followers: Attack > Prize
Distant Lands: Reserve > Victory
Dame Josephine: Knight > Victory
Ghost: Night > Spirit, Duration > Spirit
Caravan Guard: Duration > Reaction
Tunnel: Victory > Reaction
Pasture: Victory > Heirloom
Necropolis: Action > Shelter
Overgrown Estate: Victory > Shelter
Hovel: Reaction > Shelter
