If by “best” you mean cost effective then moving from mid-september to April is considered the most cost effective option. During this timeframe the demand for moving slows down and rates are lower. According to top moving professionals, peak moving season lasts from Memorial Day to Labor Day and around 70 percent of all moves occur during this timeframe.
If you don’t have any school going children or you don’t go to College yourself, you should absolutely consider this timeframe for your move to California. During this time, you will be able to land better deals and find cheaper housing.