I started with three coats of a flat gray paint to cover everywhere.. I buffed down the edges with my sander, and from there I decided to go over it with some wood stain. I used a walnut color, which gave the wood showing through a nice color, and added a vintage-y sheen to the paint. I applied it with a rag, and almost immediately wiped it off. I used one coat of water-based polyurethane to protect the finish, and I was done.
I love the look, and it was so easy to get there. Here's a picture of the chest before, after the paint was applied, and then the final product after all the distressing.