@canoehead:

I’m coming from a Risk background (and I realize there is no comparison with AA). […] given my profile so far, what is your best advice for someone like myself to have a successful and enjoyable start to my AA career?

Welcome to the world of A&A!  One thing that may help you get a conceptual handle on A&A is to keep in mind that, when you strip away most of the details, A&A and Risk do in fact have a fundamental resemblance.  A&A is powered by a “four-stroke engine” whose cycle can be described as follows:

Territory generates income

Income buys units

Units fight battles

Battles win territory

From what I can remember of Risk (it’s been ages since I’ve played it), it operates using a similar mechanic – though as I recall Risk doesn’t actually use money, and therefore Risk’s version of the first two steps I’ve listed above takes the form of a single “territory provides units” step.  So keeping this resemblance in mind as you play A&A could be helpful, both in terms of giving you a parallel with a game you already know and of helping you keep track of which phase of the A&A game you’re in at any particular moment.