You should not store zip data as an integer as they can start with 0. Zip codes use numbers, but aren't actually numbers themselves (leading zeros, no arithmetic, etc). Plus, someday you'll want to ship something to Canada.
Falsehoods programmers believe about this HN thread: it links to Django's documentation.
It linked to a 13-year-old unmaintained community wiki page, and people apparently didn't look too closely at it. I stuck a big honkin' warning at the top of the page to clarify that.
If you want to handle US zip codes, UK postcodes, or other country-specific data types in Django, may I suggest this, which formerly was bundled with Django and now is maintained as a separate add-on: