Debian has four branches: Stable, testing, unstable and experimental.
Woody is the current release of the stable branch. It is very very stable, tested on all the 11 architectures Debian supports. There are policies in place that make sure that only certain updates make it into revisions of the stable distribution (such as security updates, critical bug fixes, etc.)
I think Woody is up to r3 now (third revision). A new version of a certain application package does not just make it into new revisions, unless it fixes some critical bug. This is because a new version may also introduce incompatibilities with other packages that could cause a ripple effect of not-well-tested updates.
Testing is what will become the next stable distribution once it's released. Currently it's called "Sarge" (all releases are after Toy Story characters for historical purposes). Sarge has a completely new installer and other things. Once Sarge has gone through severe tests on all architectures Debian supports, and all "release-critical" bugs have been resolved, it will be released as stable.
Unstable ("sid", the evil boy who tied Buzz Lightyear to a rocket) is where new packages (or new versions) are uploaded to. Once they've been tested, they make it to the testing distribution. Sometimes things break in sid, but not often. Usually they're fixed in a couple hours.
Experimental is like the wild west. A place for the strong of heart. Sort of another dimension. But it's kinda cool.
So basically, if you have a desktop machine, then you probably want to stick with unstable. If you have a server, you want stable. If you're a Debian developer, you want unstable (and hopefully you have a stable machine around so you can backport packages) and testing.
I've done some Debian installs through gnoppix and Morphix as well (knoppix-based distributions, which in turn is based on Debian). These live-cd distributions do the hardware detection and much of desktop configuration (e.g. X) for you. Morphix is modular and there are several flavors available. Knoppix/gnoppix is not modular, an the installer is less flexible (i.e. it wants a strict pre-defined partitioning).
So if you want a quick desktop machine, I'd say go with Morphix.
Hope that clears things up.