Reddit mentions of Modern Philosophy: An Anthology of Primary Sources, 2nd Edition

Starting out in philosophy, I think, requires a historical approach. In order to fully understand some work (say, Marx's Das Kapital) means you need the background literature that led up to that work (say, Hegel's Phenomenology). The important thing to remember when reading through the history of western philosophy, is that all of these writers are in dialogue with one another, and that none of their views makes perfect sense in a vacuum. So, I suggest we start at the beginning.

Plato. Folks will tell you to read the pre-socratics, but if you aren't a professional or a student, it's not entirely necessary. Plato is the ground floor in terms of western philosophy and the upshot is that the dialogues are fairly easy and light reading (in the context of western philosophy, which can often get very dense). I'd suggest the Meno which covers a bunch of intro epistemology, the Republic, which covers a lot of P's political and moral thought. The trial and death of socrates is also really great. It's a collection of dialogues.

Then I'd suggest Aristotle's Nichomachean Ethics which is a direct response to Plato.

Then I'd move on to the early modern guys. Some will tell you to dig into the Romans and the medieval stuff, but again, if you just want a beginners list, I'd skip em for now.

In terms of early modern stuff, the period runs roughly from Francis Bacon or Galileo, to Kant. All of these guys are debating with each other so its important to move through it chronologically, in order to understand the context of the writings.

I always suggest that my students pick up this book: http://www.amazon.com/Modern-Philosophy-Anthology-Primary-Sources/dp/0872209784/ref=sr_1_1?s=books&ie=UTF8&qid=1375192962&sr=1-1&keywords=early+modern+philosophy+reader
Get an old edition, and a dirty used cheap one if you are buying the book. No point in going nuts when there's no difference between editions.

It is an anthology (with good translations) of Descartes' Meditations, Spinoza's Ethics, Leibniz's Monadology, Locke's Essay, Berkeley's Three Dialogues, Hume's Enquiry, and Kant's Prolegomena. Plus more- checkout the table of contents.
This book will give you the whole history of early modern, without you having to buy a ton of different books. But these are the books a beginner would read, in this order.

Once my beginner had finished these texts, he'd have a good idea of what the history of philosophy looks like, and would be in a really good position to start tackling more contemporary stuff. It will also give you an idea of what issues in philosophy (metaphysics, epistemology, logic, ethics, political philosophy, etc.) you are interested in so you can dial in what else you want to read.

Remember!: All of these books are in the public domain and you can find free copies online. The only downside is that the translations can be a little rough.

I also suggest (as you can no doubt tell by now), that a beginner tackle primary sources. People will tell you to read some secondary book that "breaks it down for you," but the only way to build up the ability to read the history of philosophy is by actually digging in and getting messy. Philosophy can be really hard to read, but you get the hang of it. But this only happens if you struggle with the text's themselves. The payoff is worth it.

Edit: /u/realy provided an absolutely badass reading list from St. John's undergraduate great books program. Check it out!!

Critical Theory does focus on breaking down traditional disciplinary walls between philosophy and the social sciences, but as /u/_kwsx pointed out, they require a large background in what they're responding to and developing to really understand or appreciate much of their work. That is, you need to understand why those walls were erected in the first place to understand and appreciate why they're breaking them down.

You can certainly do that, but it requires focusing your attention in a specific way to develop your background in the strains of thought they're interested in. This book, when read carefully from front to back and supplemented with commentary by those familiar with the authors/theories within it, should really give you a broadly firm foundation to get you started in any discipline you may be interested in. It's by no means complete or total, but it should help develop the basics for whatever you'll want to jump into that's relevant to contemporary philosophy.

Or, more generally, check out Coplestone's History of Western Philosophy. I'd probably suggest this over that to develop your interests more broadly, but either will do.

If you're interested in Critical Theory, then you'll be committing yourself to far more work than you're expecting and should plan on studying in depth the authors in that book I linked, the entire linage of German Idealism, the fall-out of German Idealism after Hegel and their methods applied to contemporary problems. That will require a large dose of people like Marx, Nietzsche, Freud, and various others. None of which are easy to understand reads

Ah no worries, he's doing it differently then. Byrne had us use this book plus a smaller book on Spinoza. To be honest though, I didn't use them that much, partly because she posted the slides and I took pretty good notes.