It really depends on what you're looking for, but Philosophy is a field where one philosopher's work is built on top of the other's going all the way back to the ancient Greek's. Its important (I think anyways) to read the raw texts before you read philosophical commentary so that you have a chance to form your own opinions. That being said, here's some recommendations of mine that cover a breadth of philosophical subjects and time periods. Its always good to see someone else want to learn more philsophy, especially if its of their own volition.

Plato. Strangely enough, Plato is probably one of the best introductions to philosophy, not only because he was one of the first whose writings survive to modern time, but also because its relatively simple to read and understand. Some of my personal favorite are 'The Apology', 'The Symposium', and 'The Phaedrus', and of course 'The Republic'. The weird thing with Plato is you'll never know how much of his writings are his thinking as opposed to Socrates teaching. I still reread Plato because the stories (most of his writing is in narrative form) are so damn entertaining.

Aristotle. This is a natural progression from reading Plato. The 'Nichomachean Ethics' is a cornerstone of ancient philosophy and is a relative simple read.

John Locke/Gottfried Leibniz. I'll admit, I struggled through 'An Essay of Human Understanding' but this title and Leibniz's rebuttal 'New Essays on Human Understanding' illustrate a historically important philosophical debate between empiricists and rationalists. Since you're reading 'Common Sense' you might also want to give Locke's 'Second Treatise on Civil Government' a gander.

Immaneul Kant. Since you're reading Schopenhauer you should read Kant as he was heavily influenced by him. You'll hear him referenced a lot if you continue to read philosophy so you should familiarize yourself with his thinking, especially on his thoughts in epistemology.

Bertrand Russell. People have already recommended him and he's one of the most popular philosopher's of modern times, mostly because he's so easy to read and was somewhat of a cultural icon during his time. I have a particular fondness for his work because when I had doubts about my faith, "Why I Am not A Christian" helped me find words to communicate my break with Catholocism. His "History of Western Philosophy" is considered a cornerstone history of philosophy book (although it is somewhat dated now). His writings are usually rather short and concise.

Jacques Derrida/Gilles Deleuze. Now we're getting into some wacky shit. To be fair, I shouldn't even be commenting on it because I have no idea what these guys are talking about half the time. These are the philosophers that people read and pretend to understand because they want to sound smart. You know the stereotypical "philosophy" students that you see in movies. Maybe you'll find something of substance in their work although many philsopher's believe these guys are/were hacks and purposefully obfuscate their writing to hide the fact that there's no substance in it.

One of the best ways to read philosophy is to start with a philosopher who truly changed the game with their work (such as Kant) and work your way out reading the work of his supporters as well as the work of those that disagree with him. This way you'll get a worldy view on 'important' philosophical issues while starting to formulate your own opinions on th ematter.