R0J0hound is right, the texture size affects memory usage and not runtime performance.
The power-of-two thing is annoyingly complicated: on desktop, you can probably forget it completely, almost all desktop computers now can support non-power-of-two textures. However, mobiles and tablets have weaker, simpler hardware and might still internally use power of two, but you can't easily tell, because the graphics card can make the support invisible (it will pretend it's using a non-power-of-two even if behind the scenes it's using power of two). TBH, I'd forget about it, it's a pain - just test your game regularly to make sure it works on mobile and you'll be fine.