I am a freshman in college and I want to spend my free time reading different works and expanding my ideas. I don't necessarily want to start linearly (from Classical Greece and on), but if that is the best way, I'd be open to it. So far I've read a little bit of Camus and Descartes, both of which I've enjoyed. I would like to start off with something more easily digestible, but a little bit of rigor goes along way in the learning process.
Some people you could read without having read from the beginning. Nietzsche, Descartes, Sartre. But if you're wanting to tackle guys like Berkeley, Heidegger, Kant or even newer guys like Saul Kripke you're going to want to go back and read Plato and read the guys from the analytic tradition like Bertrand Russle, Frege (even if he was kinda off about his ideas), Leibniz etc. The problem is you're going encounter philosophers who use words like "idealism", "monad" and other words that may or may not seem familiar and often have different meanings than what you're used to them meaning. Reading, or at least having a good understanding of, the works these guys read to come up with those words is important. If you're interested in philosophy I strongly recommend checking out the Partially Examined Life podcast. It's very informal, but very interesting discussions.
Recently graduated with a philosophy minor, and I highly recommend the site philosophybro.com when approaching the more complex works. It does a really good job of breaking down complex vocab and ideas in approachable, understandable ways. I wouldn't have understood Heidegger at all without it
Philosophybro is awesome. His Wittgenstein episode with Partially Examined Life is super interesting.
I don't have a particular route to suggest, but a resource: a good introduction to any topic or philosopher you want to dive in deeper is probably found on the Stanford Encyclopedia. These rather short articles are written by well known experts on their field, explaining the context, terms and ideas of a topic/philosopher/philosophical work, so you get a better understanding on whats going.
Before anything else, learn some basic logic and critical thinking. It makes finding the argument of a passage, as well as its strengths and weaknesses significantly easier. Patrick J. Hurley's "A Concise Introduction to Logic" is the book I used, and if you get an older edition you can get it for really cheap. After that, it really depends on what you want out of philosophy. It's a really big subject, so it'd be hard to give you a good reading list without knowing what exactly interests you. There's philosophy of science, medicine, history, religion, etc., political philosophy, and basically every other combination of an academic subject + philosophy, and more.
The contemporary introductions books are good introductions to particular branches of philosophy. Probably the best place to start would be a survey like you'd get in an intro to philosophy class. I don't know of any particularly great ones; for what it's worth, this is the book my intro class used.
A little history of Philosophy was one of my favorite reads last year. It's inspired by the format of Ernst Gombrich's A little history of the World, and is written in a similarly gentle, accessible style. I find them both charming. But then I'm a big Gombrich fan. I had this one as bedtime reading when I was a kid and I still find it immensely comforting - although I know a lot of History of Art students absolutely loathe it :/
It would probably help if you said a little more about what you're interested in specifically in philosophy. What kinds of questions grab you? Philosophy is a pretty diverse discipline in terms of topic (it's not clear to me what the metaphysics of grounding and the ideal form of the state have to do with each other), and trying to slog through stuff that you aren't interested in will probably result in your abandoning the project. If you want something introductory, I'm told that Bertrand Russell's "The Problems of Philosophy" is pretty good. You may also want to consider finding a recording of a philosophy class on a topic you are interested in somewhere, since that kind of material is pitched at a student rather than an expert. I also really don't think it's at all necessary or even desirable to go in temporal order. I'm pretty sure most professional philosophers have not read all important historical figures, and certainly not in order. Plus, a lot of historical texts are going to be very difficult to understand without guidance from an expert--I mean, even experts have deep disagreements about how to understand most philosophical texts, and I highly doubt a beginner is going to be able to make anything of Aristotle's Metaphysics or Kant's Critique of Pure Reason. No matter how smart you are, that stuff is tough.
Philosophy is an incredibly technical subject. If you grab a book from Heidegger, for example, you won't understand anything; or worse, you'll think you understand and it will seem "deep", but really you won't understand anything. The main thing to figure out is if you want to do this technical study, or you're more interested in -as you said- expanding your ideas. To read direct, I agree that Nietzsche and Sartre are good options (not so sure about Descartes). Greek classics like Plato or Aristotle are also good reads. I would also add books not written by philosophers, such as Meditations by Marcus Aurelius, pretty much a personal diary collecting thoughts, highly influenced by stoic philosophy. But for Heidegger, for Hegel, for Kant, for Husserl, get a contemporary book about their philosophy. Or at least a version of their works including good commentary by a contemporary author. Also, there is a bunch of modern philosophers that are less cryptic, usually focused on more specific topics such as philosophy of science or philosophy of language. Daniel Denett is a good example. These are also great books to read direct, but I don't think they will prepare you much to tackle the rest of philosophy. If you want to learn about philosophy as an academic discipline, and you haven't read many introductory books before, definitely start there. It will give you an overview from which you can then choose more specific topics or authors to follow. I tend to dislike university textbooks for this; those that have the "key" concepts in bold letters with a short explanation on the side, and are currently in the 16th edition... Think: A Compelling Introduction to Philosophy by Simon Blackburn looks good, but I haven't read it. It doesn't follow the history of philosophy, but rather focuses on the ideas, which I think its a very good way to do it and looks like what you wanted. Hope it helps!
If you want to dip your toes into the classics, check out Socrates' dialogues. They're available online, and you can follow them without getting very bogged down by premises. Excellent introduction both ways (linear and digestible). Try Euthyphro