If you just need to do this one task, any Arduino will do, although the Arduino Mega will be an overkill.
The limitations of the Arduino is, that has only 2kb of RAM, only 1 serial, 13 digital and 4 analog input/output pins. It's not your PC, it's a micro-controller. As far as micro-controllers go, the Arduino is a very well balanced package perfect for small to medium tasks interfacing real world things with a a few buttons or a simple lcd display. If you run into the limits, another platform is probably better. Again, for your task it's a very good platform with enough reserves for future upgrades.
With the regular Arduino based on the ATmega168 or ATmega328, you have two basic flavours, one running on 5V and one on 3.3V. As you can imagine, your driver for the solenoid will probably differ a little. Apart this, it's all up to you, whatever you like best. If you prefer a standard compatible solution where you can put shields on, go with the Arduino Uno, Duemilanove or compatible. If you're into soldering and prefer a smaller footprint, go with the Nano, Pro or Lilypads.
If the Arduino doesn't have an USB-connector on-board, (eg Pro, Lilypad), you will need a TTL to USB converter sold by exactly the same shops which sell you the Arduino. Wit the added cost of the cable, the smaller Arduino will end up costing the same as the one with on-board USB.
If you want to support the original designers of the Arduino, get the Arduino Uno.
For the coding, start here: http://arduino.cc/en/Tutorial/HomePage
For questions, you're in those forums in a good place.
And before I forget it, if your new to electronics, get a small breadboard, a few resistors, cables, buttons and leds and a sorter box to store it all to get started. Many suppliers have starter packs available with a useful selection.
Korman