Even white rice will grow rancid over time if not stored in air tight containers. My wife gets special food grade 5 gal buckets with a seal, plus she uses mylar bags and oxygen absorbers. We buy white rice by the 50# bag at the oriental grocery and store it this way.
For smaller amounts of fancy type rice she uses glass canning jars. We have a gas stove, and she will fill the jars with rice, set the lid on top without using the ring, and put these in the oven at a low temp of around 100 degrees. The air will expand but the low heat will not damage the rice. After 20-30 minutes she will screw the rings on, and presto we have a low tech version of semi-vacuum sealed jars.
Don't forget the very important step of putting your rice bags into the freezer for a couple of days before you store them to kill any little weevils that may be present.