Reddit reviews Archery Anatomy: An Introduction to Techniques for Improved Performance
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Souvenir Press
For a good explanation of the underlying physiology for why this is as described, see the book Archery Anatomy: An Introduction to Techniques for Improved Performance by Ray Axford
For some basic info, check out the getting started guide in the sidebar.
What style of bow you get will be mostly guided by what kind of bow you are drawn to (and also what you plan on doing with it). There are some decent bows in the 100-150 price range (at least in a recurve or longbow). You should probably plan on 6-12 arrows to start off with (along with a few other necessary items). Arrows can be anywhere from $5 US each on up (arrows can be found cheaper, but quality might suffer).
As for learning on your own, /u/nusensei has a good youtube channel, not sure how many videos he has on technique, but good info. Archery Great Britain had some coaching videos online, you could search youtube for those as well, I think they go at least a little into technique but might be more tuned to coaches and not the archer.
KSLInternationals website has some good info on shooting.
You can also find some good books on archery, the only one I have read is Archery Anatomy, maybe other folks here could recommend other useful books.
Bottom line is, as with any other skill, teaching yourself will likely be more difficult than if you have a teacher, but you you don't have access to one than lots of reading and watching.