Rather than write you a pretty 1,500-word essay, let's just tell you what you need to know, as quickly as possible.
Joel Hanrahan has the best specs to close in Washington, and that's who Bill Ladson of MLB.com is speculating on. Luis Ayala is the "proven vet" but he's pitched like dirt all year. Saul Rivera is around as a journeyman, long-shot type.
Will Rauch be in the closing mix in Arizona? That's Bob Melvin's call, obviously, and we'll see what he says tonight. I doubt Brandon Lyon would get displaced this quickly, but maybe there's more to the story.
In brief: Get Hanrahan if you can; even as he's the youngest possible closer candidate here, if they're going on merit in Washington, he'll get at least a shot. If you're really save-desperate and can't get Hanrahan, try Ayala. If you just like picking up guys for fun, there's Rivera. And watch Washington's next few games like a hawk (as we will).