For basic wireless router duties, get either and you're likely to be very happy with it.
Get the Airport Express: to use AirPlay to play music from any Mac, iPod, or iPhone on your network to a stereo system or powered speakers.
Get the Airport Express: to same some money.
Get the Airport Extreme: to plug in a USB hard drive for shared network storage. (Apple doesn't, and I don't, recommend you use this for Time Machine backups though--you should have the latest "tall" version of the Extreme or any version of Time Capsule for that.)
Get the Airport Extreme: to have a "Bonjour Sleep Proxy". If a Mac on the network is providing services such as Remote Screen Sharing, Remote Login, iTunes sharing, etc., this allows the Mac to go to sleep. When another Mac, iPod, or iPhone wants to use the services, the Airport Extreme will wake the serving Mac to provide them, after which it can go to sleep again. This is really nifty but probably not something you'll need for a very basic home setup. (See
http://support.apple.com/kb/HT3774?viewlocale=en_US&locale=en_US
They are both easy to configure. They both provide solid, reliable, WiFi networks with simultaneous dual-band.