The most important earnable currency is actually Marks of Favor, which you earn by completing daily challenges and by selling items you find on the auction house in Agartha.
Museum is probably not something you should be spending Anima Shards on until much later in the game.
You don’t need much in the way of levelled up gear to complete Kingsmouth, Savage Coast, and Blue Mountain.
What I did is my first daily challenge, 3 mains, 3 sides, 50 monsters, and 4 item powerups. Then I do at least 2 more mains/sides, and the 100 monster challenge. Then I open my 10 (or more) bags from the missions, set 4 matching items aside for tomorrows challenge, and sell the other 6.
That way you get enough empowers each day to handle the level, you always end up with more shards, and you’ve earned most of your Marks of Favor for the day as well.