From what I remember when my son was this age, you should not be giving your child this much milk in the day. Our pediatrician was very firm about controlling the amount of milk and juice. I think it was 12 or 16 oz of milk per day and 6 oz of juice per day. The rest of the liquid should be water. Your child should be eating regular food with you and beginning to feed himself.
My son used a sippy cup, but then we learned from his speech therapist that it was not good for his speech development. However, the straw cups aren't quite the same, because my son treats the sippy cup like it's a bottle. He sometimes asks for it in the morning and will go back to sleep. If he wakes up too early, I will go ahead and buy myself sleep time by doing this.
So, I would go for the straw cups and use them exclusively during the day. Allow the bottle if and when you think your child needs that comfort. And transition to feeding him food instead of so much milk.