Most likely you'll just need an Uno, but there are many types from many manufacturers. hell even I kinda have a couple now. The main difference between the various ones really comes down to a couple things, are they compact designs, are they reference, or are they specific. Do they have onboard USB, and onboard voltage regulator. Other then that the programming environment treats them all basically the same, and soon we will get ARM core processor support, Ah yeah baby! This is part of what has driven this platform(and a few other like it) to take off like crazy.
Then you'll need a way to interface the power portion of the timer, I have mechanical relay boards and can send you a couple if you want. You can also use SS relays but I cant send you those as I dont have any hehe. Its just a matter of hooking up 3 wires to the arduino and the positive(or load if split phase mains AC) to your load through the relay. Then a photocell, or like device to sense daylight.
Essentially we'll be constantly polling the photocell voltage readings and when the state changes enough for us, we trigger the relay. Its a nice easy project for a starter and it gives you a real use item at the end, instead of the usual light 3 leds up and say "hello world" over serial, indeed a fun one to take on
Also what tools do you have on hand? You wont need much more then screw drivers(small PC style kit) wire strippers and some catv cable and a breadboard, although it never hurts to have a good solder iron, etc...
As for the code I can whip up a little something to get you started, its really not bad at all once you start getting the hang of it, especially since the community is huge at this point.
Oh yeah, if there is anything you want fun sparkfun let me know I can pick it up then just ship it with the relay boards if you want me too send those. I assume flat rate usps covers the islands.