R.H.
You can put breastmilk in the sippy cup. Pumping is a pain...but I would hold off on the whole milk.
Cows milk can be a high allergen and typically not recommended before 12 months of age. There is nothing wrong with giving just water. Kids don't actually NEED whole milk. There are other ways to get them the fat and vitamin D that pediatricians typically want them to get from milk.
Learning to use a sippy is more about coordination then what's in it. Water is a great hydrator and introducing something like juice or flavored milk and things like that could give him more sugar then you probably want to offer.