I really can't stress how important having a few good mentors was for me. When I started I was on this forum a decent amount, thinking I could mostly do things on my own, but once I realized how much some professors really are willing and enthusiastic about helping out a pretty driven student, I leaned a lot more heavily on their advice and left a lot of the more conventional, undergrad application-type resources (books, school advisers, etc) more or less alone. Show your mentors multiple drafts, and when you get those commented drafts back, follow their advice, even if it means scrapping huge parts of your SoP or re-writing some of your sample. This also shows them that you actually value their input.
Listen to your mentors when they suggest POIs, based on your interests. Every single one of my POIs at programs I was admitted to are scholars that my mentors either suggested or green-lit. Reach out to POIs as early as (reasonably) possible. You never know how the conversation will go, what they might warn you about, or what help they might offer--the programs I was admitted to were the ones where I had the most contact with my POI and I have to imagine that's what made the difference.
Also, when possible, I would say you should try to think strategically about who's writing your recommendations in terms of the programs you apply to. Two of my recommendations were written by professors who had strong connections with my top two schools and I know for a fact that this helped me a lot at at least one school. It feels a little like cheating, but academia is an insular place and potential advisers will be more likely to take a chance on you if their friend from back in the day tells them you're a good bet. That said, the first priority with recommendations is still that they actually know you and are willing to write positive things about you.
Basically: applications are a lot more about interpersonal and academic relationships than you might think. Use the contacts you have.