power supply unit for Arduino/solenoid project
Figure out what voltages you need. You say the solenoid needs 12V, then you need to check the Arduino Duemilanove. Will it work with 12V, or does it require a different voltage.
Figure out the maximum power you will need. 12V * 1A = 12W, seems high for a small solenoid, but I don't have a lot of experience with them. Sum this for all the components you will be running simultaneously. 
Select a power supply that provides the required voltage(s), plus at least the maximum current you need. You should probably pick something that provides a bit more than what you need, because running a component at 100% is generally a bad practice.