to keep onions from being so potent that you tear up to the point you can't see while chopping, keep onions in the fridge! it cuts down on their potency and keeps them fresh longer!
also, washing your hands immediately after chopping & handling onions does NOT get rid of their scent completely, especially on your finger tips! so, before washing, rinse your finger tips with white vinegar! then wash your hands as usual and the onion scent (as well as the white vinegar scent!) will be gone!