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!