HISD options. First time mom

Hello, I am first time mom and lives in spring branch area. We are looking to buy a house in the heights for commute reasons ( we both work in the med center). My child is 14 months old so we are also factoring school zone while house shopping. A few friends told me that I can try to send my child to magnet program if my future house is zoned to a less than ideal elementary/ middle or high school.

How does the lottery work? How competitive is it? How early should I start the application process?

I did a lot of research and I am utterly confused about magnet, vanguard, the school year to apply….. etc.

We can try to buy a house in the area zoned to vanguard school, but with our budget, we would have to get a small townhome. I really would like to have a decent size house with a yard for my little one.

Thank you in advance !