moving to California
there is a term called "storage in transit".
most reliable moving companies will provide you up to up to 1 month free of charge storage: one month on each side and destination.
please note that all your things that was picked up are sitting in the storage until large moving van is coming to pick it up. so....upon that I think 2 months of storage will be good for you until you will find apartment.
good luck
Dan
moving companies
you might would like to read:
Moving to California
Moving to Los Angeles
Moving to San Diego
Moving to San Francisco
Moving to Sacramento