Your overall question is actually quite a difficult one to answer. I tried learning Astrology on three seperate occasions, the first two resulting in me giving it up (because of career pressures). I know one quite famous Astrologer who says she is on her 5th incarnation as an Astrologer.
Books are a good introduction - they whet the appetite. I started with a bit part magazine, on my first incarnation. Second time around I bought Nick Campion's Practical Astrologer. However, once again I dropped out. Third time round I was stimulated to resume Astrology by an Astrological slot on a psychic TV programme my wife watched. This time I resolved to see it through and I signed up for a distance learning course. This was not as prestigious as that Dave (Dadsnook2000) did but it did what I wanted, gave me a disciplined framework to work through. That course also introduced me to Horary and Medical Astrology which led me into traditional Astrology.
When I first started to learn, 40+, there really was only one approach to Astrology of any note - the psychological approach of character delineation. Astrology much before 1900 was seen, even by Astrologers, as being fatalistic, superstitious and full of concepts that were positively medieval. That view has now changed quite a bit. Those who practice the modern variety are increasingly interested in their tradition, even if they don't adopt the methods or philosophy. What's more their is a first cousin - Vedic Astrology, the Astrology of India, which was largely influenced by (and influenced) the Classical Greek approach of 2000 years ago. Unlike Western Astrology, it did not reach death's door and still has a rich oral tradition as well as many books.
That's rather a digression but their approach is quite different, especially when it comes to signs. so you have something of a choice that I didn't have. I'd suggest you start with the Modern approach, because there's more introductory material but with the recognition that it's no longer the only way to do Astrology.
In terms of the order of learning:
The Seventeenth Century Astrologer, William Lilly took the following order in his text book:
Learn how to cast a chart as your first step. Astrology is largerly concerned with how to interpret or 'judge' a chart so you should know how one is actually 'erected' or cast. The process is essentially the same, whatever your approach and even though you may use a computer for 99.99% of your charts, knowing how to do it manually introduces you to the geocentric view of the heavens and also teaches you something about practical geography.
Lilly then goes on to look at the three components of a chart in this order:
The Houses
The Planets
The Signs
and then a section on how these inter-relate (though nowhere near to the extent of a modern introductory book such as Parker's Astrology.
Lilly's approach is still a good one, even if you don't follow his interpretations - though these would be reasonably familiar to a modern student, apart from what would seem a bizarre view of signs, the omission of the outer planets (for obvious reasons) and the apparent lack of psychology (though it's actually in there but not in a Jungian form - again for obvious reasons).
Broadly speaking, Astrologers up to the eighteenth Century were more concerned with prediction of events (whether they consistently got that right is open to a lot of debate), rather than character delineation. So we might term their Astrology as event orientated. Modern Astrologers are more concerned with counseling individuals and thus inner motivations - though they would certainly argue that the two aims are by no means entirely separate. So another question you have to ask yourself is 'What do I want to do with my Astrolgy?'
If you want to go into Astrology in any detail, then you need to look round for an appropriate course. If, like me, you are looking at it for 'recreational purposes' then you will content yourself with looking round for one or two good books and making use of online resources.
