There are a variety of suggestions for go-bags and disaster kits. The links below provide recommended supplies, but these can be tailored to personal needs.
Go-bags are pre-packed bags, usually either a backpack or a tote bag, you can grab if you need to leave your home very quickly, or can be stored in a vehicle. These will have a change of clothes, medications, snacks, water, and copies of important documents at a minimum. Each household member should have a bag, and if you have pets that you will be evacuating with, have a bag for them as well.
Disaster kits are usually more extensive and will include food, water, first aid, and other supplies for a few to several days. People often use plastic storage bins or a plastic bucket with a lid for these supplies. These can be used either for sheltering in place, or to bring in an evacuation. They can be purchased as fully stocked kits from several retailers, but it's very easy and inexpensive to put together your own and use shelf-stable foods you normally eat that can be rotated out periodically to minimize waste. Keep in mind that power outages are common in disasters and any foods included in the disaster kit should not require cooking.
As a final mention, there are EDC Kits, Every Day Carry Kits, which are small pouches or boxes that can easily fit in a handbag or a glove compartment to deal with the more mundane emergencies in our daily lives. Many of us already have some form of this in things we always carry in our wallets, handbags, backpacks, or in the car. While more formalized among the "prepper" community, having things like a few safety pins, pencil, cash, and multi-function tool on hand can be useful for anyone.