I'm not sure Twelve Virtues of Rationality is the best place to start. To be honest, I was a bit confused reading it the first time, and it only made sense to me after I had spent some time on lesswrong getting used to Eliezer's writing-style.

For myself (as I know it was for many others), I got here via Harry Potter and the Methods of Rationality. I'd say it's a great place to start many people off, but perhaps not the majority. Along with that, what got me convinced to start reading lesswrong was my interest in biases and importantly being convinced that I, myself, am biased.

Thus I would propose one starts off with a single post about some bias, especially one that convinces the reader that this is not an abstract experiment involving random test-subjects. I think that Hindsight Devalues Science works excellently for this purpose, although it's obviously not written as an introductory essay.

Follow this up with some posts from Map And Territory, namely: What Do We Mean by Rationality, What is Evidence, and The Lens that Sees its Flaws, in that order, to give a basic introduction to what rationality actually is. This could be followed by one or two more posts from Mysterious Answers to Mysterious Questions, so why not start with the first two: Making Beliefs Pay Rent in Anticipated Experiences and Belief in Belief.

Now, you could finally digress to Twelve Virtues Of Rationality and then maybe try your hand at the whole Map and Territory Sequence (skipping over those posts you've already seen), alternatively you could finish reading the Mysterious Answers to Mysterious Questions sequence first.

After this, I no longer provide any advice as to reading order. You could choose to follow the order provided by XiXiDu above. I provide the following as one order which would at least do better than picking articles at random:

Finish reading Mysterious Answers to Mysterious Questions if you haven't already done so.

The whole mega-sequence of How to Actually Change Your Mind contains a lot of pretty important stuff, but will take a while to read.

The rest of Lesswrong. ;)

Summary:

• Hindsight Devalues Science
• What Do We Mean by Rationality
• What is Evidence
• The Lens that Sees its Flaws
• Making Beliefs Pay Rent in Anticipated Experiences
• Belief in Belief

And then follow with either of:

Path a

• Twelve Virtues Of Rationality
• Map and Territory Sequence
• Mysterious Answers to Mysterious Questions Sequence

Path b

• Mysterious Answers to Mysterious Questions Sequence
• Twelve Virtues Of Rationality
• Map and Territory Sequence

Which concludes my recommendation.

For anyone interested, I've made an ebook variants for myself (epub, mobi, PDF, odt). It is far from awesome, but at least readable on e-book reader. https://www.dropbox.com/sh/6agp4otiukejb0g/AACO-5V1J8i0USBWUFL9nw74a