a few pieces of advice from my experience:
1. don't worry about the GREs. i have spoken to faculty who don't even know how many total points are on the GRE (seriously), let alone what constitutes a good score. my impression is that it can be disqualifying if egregiously low, but otherwise no one cares (actually, that's more than my impression. i have explicitly been told this). i do, however, recommend taking at least one practice GRE before you actually sit for the test. i didn't do this, and i found the experience of taking the test on a computer stressful (there's a countdown clock ON THE SCREEN as you're taking it, which created a lot of weird psychological pressure for me. i also tend to skip around a lot when i take tests, which isn't possible to do on the GRE given its format. this ended up requiring a big, impromptu adjustment in my test-taking strategy, mid-test, which didn't help with the whole psychological pressure thing). but definitely don't make the mistake of thinking the GRE is anywhere near as significant for your PhD applications as the SATs were for undergrad. it's not.
2. application fees are expensive, so ask for fee waivers whenever and whereever you can. i only applied to 6 schools, and got fee waivers from 2 of them, just by politely saying i didn't make a lot of money at my job. some schools will ask for your tax returns- you can decide if actually sending those is worth it to you. but this is a seriously easy way to save hundreds of dollars during the application process, which will be especially useful if you apply to 10+ schools.
2b. on that note, i might be a bit of an outlier on this forum, but i kept my list of schools i applied to really tight. why? because i didn't want to spend money and time applying to a school i knew i wouldn't want to go to. think about what your priorities are. for me, i didn't apply anywhere i wouldn't want to live. for example, i know arizona is a great school (and i would have been extremely lucky to be admitted there), but i have no interest in living in the desert so i saved myself the $100. if you know in advance that you can't imagine moving somewhere, don't bother paying them to read your application.
3. your writing sample is definitely the most important part of your application. have a good one. ideally, have one that one of your letter writers gives you feedback on.
4. people give various kinds of advice about whether to "name names" in their statement of purpose (i.e., name who you want to work with in the department). i ultimately didn't, and i think it was the right call. no matter what you know about a professor's work, you probably don't know 1) if they're taking on more students (they might have an upcoming sabbatical, or a full roster of advisees); 2) if their interests haven't moved in a different direction (specifically one they haven't yet published much on); 3) who's on the adcomm. imagine a case where professors x and y both work on z, and you write in your letter that you'd love to come to school a to work with x on z. lo and behold, y is on the adcomm. they may well feel slighted that you don't want to work with THEM, and that could color how they read your application. i think it's much safer to just say you're interested in z. besides which, who KNOWS who you'll end up working with? this is often far from obvious several years into grad school, let alone before you've even started.
5. it's a long and stressful process, this admissions thing. try not to put too much pressure on yourself (hard i know), and try not to let your self worth get tied up in what schools accept or reject you (this was even harder for me). best of luck!