I'm going to assume hockey doesn't count for the sake of argument.
Uhmmm, I think I would go downhill skiing (the original one, not super G or slalom or anything, forget if it has a different name) for Winter.
And 4x 100 relay for the Summer. The 100 event is the king of the games IMO, but I'll assume I'm only good enough to be in the top four for my country.