Which Arduino to buy, and what to power it with?

I have not measured it because it's still in the planning stage, nothing is assembled. I'm trying to get input from people who know more than I do before I buy a bunch of things that won't actually work for my project. I don't know much about the arduino and its capabilities, so I'm not sure how much power I'd even need to make the thing run, or even how many LEDs would be lit at the same time without visible flickering.