No you don't - what more kit do you need? I've got one sat here, nothing attached to it apart from the feed from the wall and it's mains power. It appears to be working beautifully.
The Airport Extreme does not have a DSL modem in it. It has a WAN port for connecting TO a DSL or Cable modem. See
http://www.apple.com/airportextreme/specs.html.
If the Airport Extreme is plugged directly into your wall and working great, then the Airport Express would likewise plug right into your wall and work great. See the Airport Express tech specs here:
http://www.apple.com/airportexpress/specs.html. Note that there's very little difference between the two. Let me highlight the differences:
1. Express is draft-n not final-n for Wireless; this is a certification difference, though, and I've never seen something not work on Airport Express which works on a final-n spec base station.
2. Extreme can use 2.4GHz and 5GHz at the same time; Express can use one or the other.
3. Express can handle higher humidiy (90% vs 80%), although, again, this is primarily a paper difference.
4. Extreme has three LAN ports (the only LAN connection on the Express is the wireless)
5. Extreme's wireless can support 50 connections at a time, while Express can only support 20.
6. Extreme supports a hard drive connected to its USB port.
7. Express can connect to a speaker to stream music via AirTunes.
8. Extreme supports "sleeping" Bonjour services on connected computers (ex, computer can go to sleep and another computer will still be able to connect to its iTunes service, waking it only when needed); with the Express you'd need to never allow your computer to sleep for always-on Bonjour services.
Seems pretty cut and dry. Unless you're taking advantage of one of those differences, you'd be just as well off saving money and getting the Express.