I actually think the eyes in the example that you've given look a bit strange - they look too wide to me. I know what they're going for, kind of the big innocent baby eyes - but I don't think they've pulled it off - it just looks like her eyes are going to fall out the side of her head...

I think you just need to make sure you decide on the size of the eye first and then use a sphere as a temporary stand in, while you model the geometry around it. when it comes to animating the eyelid, i'd guess that a blend shape would ensure that you don't have parts of the eye sticking out - if you do then it's a case of adding more geometry. at the end of the day, when you're eyes are open, the lids are bunched up, so it makes sense that you would need more geometry when you close them.

er... hope that helps.