There are several good anthologies (in book form or online, free or commercial) that are particularly nice when starting off and orienting oneself and finding one’s bearings within the suttas and teachings:
- “A Self-guided Tour of the Buddha’s Teachings” online on Access to Insight. This goes through all the main points of the dhamma using the “gradual training” structure (often used by the Buddha himself). Check out the rest of the site too.
- “In the Buddha’s Words” by Bhikku Bodhi (as mentioned already by SarathW1). This is fairly cheap to buy, but you can read all the suttas in it here for free and the introductory parts to the chapters are here also (just go to the Reading Guide section of this site and scroll down to the end of the page).
- “The Word of the Buddha” by Nyanatolika Thera (online and free). This is a very nice sutta selection of suttas structured according to the four noble truths with the larger part devoted to the fourth one (the eight-fold noble path). The BSWA also hosts a nice series of videos here by Ajahn Brahm where he gives a series of talks working his way through the chapters of this book. Check out the rest of the BSWA website for lots of great uplifting dhamma talks (EDIT: just see now that Kay has recommended these also).
- “The Buddha’s Path to Deliverance” by Nyanatiloka Mahathera (online and free). By the same author as “Word of the Buddha”. It’s longer and more detailed and uses a different structuring scheme (the three-fold training: morality, concentration and wisdom intermixed with another more obscure scheme called the seven stages of purity). Another good overview of the teaching. Contains a good overview of the main meditation practices also. It’s my favourite of the two, but it’s probably better to have read one of the earlier intros before reading this.
If you like audio (which I do 
), Bhikkhu Bodhi’s series of 10 downloadable introductory lectures “The Buddha’s Teaching As It Is” is very nice, which covers:
- The Buddha
- The Four Noble Truths
- The Nature of Existence
-
Dependent Origination
- Rebirth and Kamma
- Nibbana
- Eightfold Path
- Meditation
- Social Teachings of Buddha
- The Sangha
For a short concise run-through of the main concepts and ideas associated with Buddhism, probably the best list I’ve seen is here. Unfortunately, this is on a rationalist/skeptic site, but, for the most part, gives a fairly balanced overview and isn’t too hard on Buddhism. It doesn’t pull its punches at a few points (maybe even somewhat deserved at a few points). It’s a good summary list though (though far from as comprehensive as the dhamma concepts chart linked to by SarathW1).
If, at some point, you start reading the suttas themselves, then probably the Majjhima Nikaya (MN), for various reasons, is probably the best place to start. Particularly, at the start, you’ll probably find often yourself being a bit puzzled at one section or another. However, Bhikkhu Bodhi has a whole series of talks on the various MN suttas (part of a course he gave on the MN with a suggested reading-order plan of attack). Nice if you want to have a whole sutta gone into in detail by a real expert with often useful student questions answered at the end also.
On Dependent Arising (DA), it’s probably good to try to get an intellectual understanding of this (though it’s a difficult teaching). However, I suppose the end point is to eventually go beyond intellectual understanding and gain a direct intuitive knowing/insight into DA. The idea is to work the eight-fold path until you get to a stage where that’s possible (where the five negative hindrances have been sufficiently weakened and where morality and the necessary seven positive qualities, the factors of enlightenment, have been sufficiently strengthened). But that’s pretty advanced. A person who has seen directly into DA like that, according the Buddhist teachings, has actually become a stream enterer (the first of four stages of enlightenment). That’s the first taste of nibbana (just a glimpse). The remaining stages, I guess, are then the concrete (and inevitable, according to the teaching, all within seven lives) working out of the implications and consequences of that insight. I suppose that’s roughly where DA fits into the overall big picture.