AP is unlocked through the Avatar Boards.
I would suggest unlocking the first two nodes on each board (should be one AP and one Cost) and moving on, unless you really want costume parts.
Story Quests give you 150 jewels every five levels, it is finite, but it should fuel you well at the start.
Ten pulls are generally a gyp (less so when there's a guaranteed "epic" medal, but eh), stick to Daily Draws for the most part.
Oh? Why are ten pulls a gyp? I just did one and got 5* Alice and a bunch of 3* and a couple 4* medals. Still learning exactly what the medals do and all. I assume its basically like rarity in FFRK.