When peeling sweet potatoes, should I just peel the outermost layer, or should I be peeling off the white part as well till I hit the orange inside? Should I keep going until it's all a darkish orange?
It doesn't really matter.
A lot of people cook them with peel still on and peel it with their hands when cooked (Careful, hot!). You can peel them before you cook them, and then it's just a question of taste I'd say.
Personally, I would peel off the white as well, though I'm not sure about this.