be careful with trusting realtors, zillow or mls to tell you which school district the house belongs in.
It is best to look up schools you like (maybe start with greatschools.org). You can see the rating and also read the reviews (a lot of times people with extremes will complain or praise the school). I would then call the school districts you think would fit you and your family.
I have never heard of a school not accepting someone who lives in the school district to not be allowed due to over crowding, but the after school programs book up really fast. Also some kindergartens are half day and your child may get 11-2:30 or 8-11:30 (i filled out the early request in March and didn't heard back until a week before school started). This could be important to you if you work.
You also should ask your close friends and family who live nearby. Once you get a few names of schools from people you trust you can start contacting those districts. Your state could be different, but the realtors in CA say 'This house is in a great district.' even if it is not because they are trying to sell the house and or neighborhood. They have also been know to say a house belongs to a school district that it does not belong to (maybe a lie or maybe they just assumed wrong).
Private school is also an option (if you have the budget). This could remove the stress of making sure the house is in a district you like.