Having lived in Southern CA. We had fire, riots and mud slides to contend with.
For a fire or Twister, I would try to throw as much as I could into the truck/ SUV to save.
As far as Ammo to take. Easy enough to run the AR and a 9mm Handgun. I say that as trying to drag as much stuff as i own I want to take with me light weight stuff. 200 rounds of 223 weight the same as 50 for the 308 and I can almost double the amount of 9 for 45 ACP. I also keep a few MRE's in a go bag. Enough for 7 days with ammo next to a case of water (and a few Diet Cokes if I do not have one by 2pm I get caffine withdrawls) And a couple of hundred $ in small bills just in case. I don't think the ATM will work for gas or other if I need them to head to friends outside of the problem area.
For a riot. I would look to store water and fire extingushers and hole up in the house. A safe room can be made if you fear people shooting into your house.
Bad thing to be leaving and turn the corner to find the riot there an headed to you. The good/ or bad thing about a riot is they do not last long. Super markets have about 3-5 days worth of food on the shelves. A riot will empty a store and will peter out as they look for food, water, and money. While a roit is going on there is not going to be deliveries of food, water, medication, or money into the area.
So I would stock up on enough water for a week and rotate the bottled water out so that you will always have fresh. and keep enough to last for a week for your family as well as dry or canned goods to eat for the same week. If you have any medicine you need I would also keep a weeks supply on hand as well. Same would go for a flood or other natural disaster. At my parents house in NC for Huricanes, we have placed Medicine, spare glasses for both of them, food, water, dog food propane, and charcoal at the barn 10 miles inland just in case they have to leave the house. All the camping supplies are there as well so they have tent heaters, stoves, cook ware and bedding not to mention Dad keeps his boats there when not in the water so they have the Cat boat as well for shelter and a generator if something were to happen to the barn. They too rotate the supplies from the barn into the house on a regular basis to keep everything fresh. They live about 3 hours from a Cost co and go once a month so they take either Dad's Truck or suburban and get stuff for about 3 weeks.