As a philosophy major, I would advise you to pay attention to the order in which you expose yourself to materials. The earlier stronger impressions in your journey will naturally have a weight on your opinions of later materials. In addition, academic departments usually have an -ism bias so that will also influence their content recommendations.
A neutral starter would be:
Introduction to Logic and Critical Thinking
Once you have some formal thinking tools, I would approach philosophy building organically by writing down your beliefs and identifying questions and gaps, and then researching those ad-hoc. You may also discover that your current existing informal / intuitive model is mostly sufficient for a 21st century life.
"A neutral starter would be: Introduction to Logic and Critical Thinking. Once you have some formal thinking tools, I would approach philosophy building organically by writing down your beliefs and identifying questions and gaps, and then researching those ad-hoc"
There are probably many HN readers who would find this a congenial approach, since there are so many programmers here, and logic is so close to math and programming.
I also can't deny that studying it does make one's thinking more rigorous, and it's useful for working with other philosophy (and with math and programming).
However, I am concerned that someone who starts off with logic might get the impression that that's what all philosophy is about, or that's what it builds on, and just stop there. While that's true for some types of philosophy, it's not true for the majority of philosophy.
Also, for those people who aren't in to math, logic, puzzles, or programming, I'm not sure this approach would be particularly engaging for them.
When starting from the Socratic dialogues, I think pretty much everyone gets engaged, since they deal with questions which are of universal concern. They are also questions and themes that run throughout the whole course of Western philosophy (and many in Eastern philosophy too, though from a different direction).
People who start with Socrates instead of logic might not have the tools to analyze his arguments rigorously (though if that's even possible is debatable), but they'd get a much better feel for what philosophy was about.
I would agree that Plato/Aristotle are good foundations for understanding European intellectual history but a lot of chronological study is required to see their influence / relevance today. Here's a cool dependency graph that shows the centrality of Ancient thought: http://www.designandanalytics.com/philosophers-gephi/
However, I worry that a student without some grasp of valid inference would be at the mercy of aesthetic attraction/repulsion factors for deciding what to accept as valid.
I specifically recommended "Introduction to Logic and Critical Thinking" because I found it to be the most practical and skill-based class in a Philosophy curriculum. While they usually cover some proofs, most of the content has to do with identifying arguments. In addition, having knowledge of formal/informal fallacies helps in everyday inference. It is also relatively free of heavy "Greco-roman" western bias, which may appeal to a wider audience.
There are many great recommendations of philosophy works to read, but logic itself is how philosophy works. I would even go as far as to say logic is the class that has had the single largest impact on my life.
A neutral starter would be: Introduction to Logic and Critical Thinking
Once you have some formal thinking tools, I would approach philosophy building organically by writing down your beliefs and identifying questions and gaps, and then researching those ad-hoc. You may also discover that your current existing informal / intuitive model is mostly sufficient for a 21st century life.