If you leave the 12V supply permanently connected to the mains, you can control the 12V pump from the Arduino using a logic-level mosfet, a gate resistor and a flyback diode. See http://bildr.org/2012/03/rfp30n06le-arduino/ for the connections, however it's recommended to connect a resistor of 100 to 220 ohms in series with the mosfet gate terminal. You can power the Arduino from the same 12V supply.
If you want the timing to be accurate then you will also need either a real-time-clock module, or a 60KHz time signal receiver module, or an Ethernet connection so that you can access an NTP server. Alternatively, instead of using fixed times, why not add a light sensor to your project? Then you can turn the washer on at dawn and and then at (say) 5 hour intervals until dark, and the system doesn't need to know the time.
To turn on the system whenever you want, why not just add a push button?
I'm looking at your provided link right now.
I can't press the button, because the camera(s) are off-site.
They're all spread out geographically.
So my idea is to do it remotely.
I also changed the idea of having the cycle start automatically, because there are days when the camera doesn't need the wash.
And I would be "wasting" that water inside the reservoir.
So that's why I think it would be better to remotely connect to the Arduino, and turn on the wash system cycle when desired.
Which Arduino board would you suggest I buy?
I see that there are like... 24 in SparkFun.com
Any thoughts?
I suggest this http://arduino.cc/en/Main/ArduinoBoardEthernet then. You will also need a 2-port Ethernet switch that supports POE both for the switch and for the attached devices (if such a thing exists), unless you double up the Ethernet cable.
Yes, that is an Arduino Ethernet. Btw there is also an Ethernet Shield which is for adding Ethernet to a regular Arduino - perhaps that is why you were confused.
I just bought my first Arduino Uno board.
(no shields yet. Also, it's the one with the Atmel chip in the "cradle" (name??). Not the new one that has the Atmel chip soldered on (SMB?))
Anyway, I got a couple of other items, yet I'm at a loss as to how to connect all this.
I think I'm missing various components before making this work.
Using the mosfet as shjown in that diagram, you should connect a 100 or 220 ohm resistor between the Arduino output pin and the mosfet gate. If you substitute a TIP120 for the mosfet then you MUST connect a resistor between the output pin and the TIP120 base terminal. 1K will do. The disadvantage of using a TIP120 is that it has a voltage drop of around 2 volts, which means it will get hot and need a heatsink unless the motor current is small.
Unfortunately, the IRF510 is not a logic level mosfet, it's designed to be driven from 10V on the gate instead of the 5V that the Arduino provides. With 5V on the gate, I wouldn't ask it to pass more than 500mA. Look for a logic-level mosfet instead.
Unfortunately, Radio Shack appears not to stock any logic level mosfets in its stores. You're not alone, here in the UK, Maplin is equally useless.