Dressers? Is it a must for baby?

Alicia
Help! 
So I'm planning the nursery and it will be in a small bedroom with a guest bed as well. The guest bed isn't huge, it's just a day bed, and honestly we're probably going to get rid of it after the baby is born (I'm keeping it for now because my dad will be here along with my in laws for the birth, so we need both guest beds). 
Now here's my dilemma. I don't plan on getting a rocker, at least not right away. 
Baby will more than likely spend at least 1-2 months in our room in a bassinet while we adjust to being new parents.
My space is limited, I have room for the day bed, crib, and a dresser. That's it. 
My original plan was to buy a dresser and get a changing pad top for it, so its dresser+changing table in one. 
My question is: do you NEED a changing table? Seasoned moms, did you even use it? If so, how often? 
Or could I get away with getting a shelving unit with some of the storage baskets from target and putting it in the closet with the babies other clothes? I don't want the room to feel too cramped and we live on an island in Hawaii so my options are VERY limited with store selection, price and shipping options.