Thanks, everyone for your advice, I don't have anything yet, it is much appreciated (My plan was to work out what I needed then order it all at once — I don't live in a country where you can just drive down to the store to buy these things). I didn't mention the additional functions as I really wanted to start simple and work up.
I've been reading about the Neopixel strips recommended. Although they are more expensive, it does appear that you can simply connect them to the arduino directly which is very appealing. So I am now torn between paying a bit more for simplicity or trying to use a mosfet of some sort. I think I'll start with the Arduino nano + Neopixel's as a first project, then move up to creating some circuits for cheaper longer light strips. (It looks like the nano has a lower memory version and a higher memory version, I think the Neopixel strips need a uno if you want up to 500 lights)