Hi,
This should be pretty straight forward, if you only want one device to be made, the best route is to use an arduino + a shield that allows it to connect to the internet, such as the ethernet shield. The arduino would then check for new tweets and act accordingly on its outputs. It could also tweet back to produce some feedback if needed.
If you need several then maybe a custom PCB is the way to go: higher developing costs (one-off), but smaller hardware costs.
I am in Australia (currently in Melbourne), just in case this makes things easier.