Neil, you can elect to create either a new network with the AE as its "base station" or you can join your existing network with the AE acting as a kind of "repeater." I have done it both ways but the nice thing about adding the AE to your existing network is that it extends the range of your network. The basic instructions are in the AE manual.
The wild card is the Netgear router; I have no idea if there are problems associated with adding an AE to a Netgear network. A little Googling should clear it up if it seems to be a problem...
I doubt that there is something wrong with the AE... Connecting to a new AE wirelessly in order to set it up has always been a hit-or-miss affair in my experience. I have found that connecting to the AE via an Ethernet cable is the most reliable method. When you are done configuring the AE just move it to its new location near your audio system.
An Airport Express is just a small wireless gateway/router like your Netgear. If you elect to have the AE join your existing network the music will be sent to the AE from your Mac via the Netgear router. If you create a new network then the Mac will be sending audio directly to the AE.
In order to greatly improve the utility of your new Airport Express I highly recommend getting
Airfoil. Airfoil makes it possible to stream audio from any source on your Mac, not just from iTunes. As I am typing this I am streaming Gregorian chant playing on
Pandora throughout our house. It is streamed from Safari via our Airport Extreme Base Station to the AE connected to our living room sound system. A Recoton transmitter connected to the receiver sends audio to wireless speakers in various rooms. Airfoil even makes it possible to stream audio to other Macs.
It's too bad that you aren't running Leopard... If you were we could connect via iChat and I could not only see in real-time what your settings are, I could input the settings myself! Transcontinental hands-on tech support is a reality in 2008. It's even possible to drink a pint or two together via the Internet, although it isn't quite the same as sitting by the fire in a cozy pub...
(Of course, those not running Leopard can use
LogMeIn to remotely control Mac via your Web browser. I think that the LogMeIn plugin only works with Macs running 10.4 or higher. You can even control a remote Mac using an iPhone. And the basic service is FREE!))