As a general rule, your (US-based) standard car insurance will cover basically the same things for a rental car as it will your own vehicle.
You have obviously decided that the liability limits (ie, those covering damage to others) on your private policy are sufficient when driving your own vehicle, so we can only presume they are also sufficient when driving a rental car.
Personal injury (ie, coverage for yourself) would normally be covered by your personal medical insurance. But again, this will be exactly the same situation as for driving your own car. If you do not have personal medical insurance you may wish to take out the Personal Accident Insurance to cover this.
Personal effects (eg, your luggage, etc) will sometimes be covered by your home contents insurance. Once again, same as for your personal vehicle. If you do not have home contents insurance, or if it doesn't cover you for contents in a rented vehicle then you may wish to take out Personal Effects Coverage - but odds are it's not worth the cost.
This leaves damage to the rental car itself, which it's not clear from your screenshot if your AAA policy covers or not, however if it doesn't then your credit card will cover this damage up to the limited listed in the policy (which isn't shown in your question).
So in general, you likely do not need any additional coverage.
Obviously this statement is based on the very minimal information you've provided, and only you know your exact situation especially around the specifics of your various policies, so if you require confirmation of anything above you should either read your insurance policy document(s), and/or contact your insurance company or broker to confirm the details.