help to choose a part

I'm building a 5x5x5 led cube driven by an arduino uno. I've been watching http://www.instructables.com/id/Led-Cube-8x8x8/ as a guide. I think they use 2n2222 as switches to connect the 5 layers to ground. Are these the best choices? would they "overexert" the arduino pin and cause too much current draw on them? each given layer at its peak could draw 200mA. Or is it perfectly fine because the arduino's digital IO pin is connected to base, and the emitter has no load on it (is connected to ground)? would I be better served to use a N channel mosfet? if so which one? why are so many mosfets rated to handle hundreds of volts? when I try to simulate this on everycircuit.com/app/ then i get uA of current coming off the drain. Or how about a relay? Isn't a relay whats truely called for? but relays are so big and clunky. do they have any sort of millisecond delay during switching? that'd be a problem. I'm shopping at leeselectronic.com if you can suggest any part. Or maybe (hopefully) I gave away some of my ignorance about electronics in my questions and you might better educate me.