I am looking for a short, concise resource that will help me better choose and use typefaces.
I think the ideal resource would have a thoughtfully chosen list of about a dozen of the most important typefaces. Along with this, it would include basic instructions on how to use these typefaces.
Perhaps a slightly oblique answer, but I recommend you buy The Non-Designer's Design and Type Book by Robin Williams. There is no better resource, and you'll find all the answers you need to get you rolling, both for typography and layout. This is especially true for the "instructions on how to use these typefaces" -- that's a book length answer inappropriate here.
That said, you don't need as much as a dozen. If you sift out a couple of sans, a couple of serifs and a couple of scripts, you'll do better. You can always expand your type "vocabulary" as you gain experience.
If you're working with one of the Adobe Creative Suites you have Minion Pro, a great workhorse serif face and Garamond or Caslon for a traditional look. Bernhard Modern also works very nicely for more decorative work. For your second sans, Futura is probably a good choice with a multitude of uses; its close relative, Century Gothic, comes with your computer. Myriad Pro is a highly readable workhorse sans that's also good for headings and works well with Minion. Bickham and Caflisch are two very different scripts with a broad range of uses.
On the Mac, you have Helvetica (not great for extended reading, but very respectable for headlines) as a second sans, and Lucida Grande (similar to Lucida Sans Unicode on Windows) as good sans choices if you don't have the Adobe fonts.
Behind these suggestions is another consideration. Your workhorse typefaces should come in a good range of weights, which makes them much more versatile. It's best to have a Light, Regular/Roman, Semibold, Bold and if possible Black/Ultra-Bold in any one sans. For serif faces a semibold is very useful, and an extra-bold is occasionally handy. Condensed, and occasionally Extended versions can also be very useful (please don't stretch or compress a regular typeface!).
This is a difficult question to answer. This is an art, not a science, and there are no hard rules. Every rule has a counter-example which is arguably successful. Many successful rule-breaking forays are things which the previous generation would have thrown away rather than submit.
Regarding typefaces use, the old rule is that 3 typefaces is one too many, or "never use more than two typefaces in a design."
Regarding layout, the most common rules that people use are grid-based, but the size, style and resolution of the grid is really up to you, so that's more an arbitrary personal tool than a rule. Some people like the golden ratio, which is fine, but the halo of magic around this ratio is pretty much BS. The idea is to use a scaffold or structure to help you make less-than-arbitrary placement choices.
Regarding good typefaces, this is also a matter of taste, but Helvetica and Garamond are huge and full of tradition. Gotham is very popular now. Times and Arial will do in a pinch. Some will scoff at this, but there is a funny web site which quizzes people "helvetica or arial" ( http://www.ironicsans.com/helvarialquiz/ ).
I am sure other can add to the list, but probably wiki territory.
It's directed at lawyers, but is really good at explaining the typographic world in layman's terms.
I linked to a page that talks about font recommendations, but the nav on the right covers a lot of different elements of typography.
