Arduino
I've been working with them for some time now.
The Uno seems to be the Duemilanove, and most are based on the Atmega328 chip. I would recommend the two just mentioned. The also sell Mini's which are great for things like helicopters or anything that requires less weight and space. Some Mini's have a usb port on the board, which makes it so much better to code. Others w/out the usb port require a programmer, or a host board like the Uno to program it. They also make a Bluetooth board that can be programmed wirelessly, but it cost between $100 and $150; while the other boards from $10ish to $30ish.
If you want to stay in the networking aspect of it, the Ethernet and WiFi shields are a must. You can run your own web servers from them, making it easy to interface with a smart phone.
The LCD shields are also kinda cool. I'm currently building a mock Times Building(New Years Ball Drop) for a friends kid. The LCD makes it easy.
Another cool shield is a GPS logger shield. It great for automotive hacks. And it has a slot for SD cards.
I have an MP3 shield, but don't really use it for anything.
If you've never done any embedded stuff I'd go with the Uno or Duemilanove. Code for Arduinos are called sketches and are watered down C++. HackADay.com has a great tutorial series on coding AVRs.
I would go with the second one. You could do more with it, mostly because of the IR receiver and transmitter. Plus it comes with the LCD Shield. Although you could easily hack a remote for the same functions. The first one is a good starting point for absolute beginners. But if you have experience with code and a basic knowledge of the solid state world the second one would be the best option.