I take back almost everything I said about the game being linear.
After getting to The Gulch and beating the boss there, I was wandering through Majula and
In other words, it's clear that I've been going down multiple, separate, equal paths leading to places that might progress the story and might not, but I'm having a great time.
After getting to The Gulch and beating the boss there, I was wandering through Majula and
found an itty bitty path before the town. I used a fragrant branch on a stone woman expecting to get a ring, and now I've begun what might be the longest path yet.