First, most natural disasters happen so quickly that one is not given twelve hours notice to evacuate.
Everyone should have an emergency box set up with non-perishable food, bottled water, flashlights, extra batteries, battery-powered radio, first aid supplies, etc. and pack that to go first. If you take any type of medication regularly, that needs to go into your personal tote bag, along with money, credit cards, insurance cards, and other small personal documents you may need. Important papers should be included. Next comes clothing, but realistically, the entire wardrobe couldn't go. Choices would have to be made.
The most important things I would want to save would not take up much room: photographs of my family and friends, plus mementoes that hold special meaning for me. It's a good idea to scan special photos and save them on flash drives that use very little storage space. Duplicates should be kept in at least two places in the home where they can be reached quickly and popped into a pocket or tote.
Some disasters, such as a sudden tornado or house fire, destroy a home so quickly there is no time to save "things", and it's much more important to prevent loss of life. Most material things (other than those photos and mementoes) can be replaced. In addition to using flash drives for photographs, t's a good idea to give copies of your special photos to other family members so if yours are lost, they can be replicated from the ones you shared.
Given twelve hours advance time and a truck, I could take anything I would not want to lose, but that would be luxury, not realistic in the face of an impending disaster.