Hello all,
I'm a professor in a "top twenty" English department. I've served on the graduate admissions committee off and on for more than a decade. Let me quickly answer some of your questions:
GRE scores matter a great deal for initial cut offs. We get something like 300+ applications every year. A third of those or so are tossed immediately, based on a combination of low GREs, low grades, and a quick read of the materials. GRE scores continue to matter further on down the line, but become less important. I have seen low GRE scores kill a candidacy even at the late stages (when the writing wasn't enough to compensate). However, I have never seen high GRE scores by themselves admit anyone. WS and SoP matter most of all. SoP should be a concise, clear, and jargon free explanation of why want to go to graduate school in English. Above all else, it should be intellectual. You should make it clear that you aware of and interested in the state of play in contemporary scholarship. Common errors are the "I love literature" essay. We all know you do, but that is beside the point. Or the "I want to write a dissertation on topic x" statement. We all know that you won't write that dissertation. Try for a simple, intelligent, and above all well-written explanation of what kinds of topics and questions in literary study you find compelling and want to pursue. And yes do explain what about graduate program x (what faculty, for example) interests you. WS should simply be the best piece of writing you have. That is not very helpful I'm sure! But there really is no other way of putting it. Your professors will be able to tell you what among your work reads the best. Take the time to improve, polish, and get to the right length your best paper or thesis chapter or what have you. Everything else being equal, it's better if the sample is from the period you declare as your field of interest. That is, everything else being equal, if you're applying to work in the nineteenth century, you shouldn't send an essay on Chaucer. Letters of recommendation matter less than you might think, given rampant puffery, but they still matter some. Your professors should be able to make a good case for you. So make it clear to them that you know why you're applying to graduate school.
Finally yes, it's true that admissions are competitive. There is no magic bullet to get you in. Admissions committees look for curiosity and intelligence and a clear potential to produce good work in literary studies. All we have to go on is what you send us, so make sure that material is in tip-top shape.
Happy to answer any additional questions you folks might have and best of luck.