Most of my life I've been very, very unintestered in philosphy but I've recently developped a curiosity for some philosophical concepts like "structuralism" and I'm a bit curious about what the fuck type of political philosphy the Greeks developped after a friend told me they were reading Aristotle for their poli-sci class. What should I read? No self-help books please and thank you.
People already mentioned Bertrand Russell's books. They are good starts.
As stated earlier in this thread, epistemology is a good start. I've always thought that for the every day person, a lot of politics is an epistemology problem. And if you want to get into Zizek, you'll learn that it's a psychoanalytic problem.
If you want to get into continental philosophy, I wouldn't dive too deep into anything at first. Just read broadly and use wikipedia, iep, and stanford encyclopedia of philosophy in that order. Wikipedia explains it all for the general person, Stanford explains it all for the more experienced and is more in depth. I'm also biased but I feel that continental philosophy is better suited for politics since Marx is part of that tradition.
You can use those encyclopedias to read Plato, Kant, skim Hegel (he is dense and is basically a meme among philosophy students for his denseness), then you can go into Marx. You should be okay from there. No one is an expert in everything and it's basically impossible to retain and absorb everything , don't get anxiety over reading any philosophy. Although I can't say anything for your existential anxiety.
edit: and if you want lib shit, read John Rawls.