I was in the same boat and everything I had were still valid. There really is no time constraint in updating your status.
Most important is going to be your passport. This will give you a backup proof that you are now a US citizen, in case you misplace your NC.
First thing that is not resource intensive on your end is to schedule the appointment with USPS to get your US passport. Submit your application, your photos (some USPS has the option to take your photo as well), and your Certificate of Naturalization (original). Set and forget, until you get the certificate and your passport back.
Next is your driver's license or social security.
If your driver's license is still valid, I would leave that alone until you need to renew.
For social security, fill out the application and put in a piece of paper that you just need to update your citizenship. Depending on your local office, they may ask you to come in or mail in your passport and other proof along with the application. You should call your local office and find out what the process is.
Unless you need to claim social security benefits immediately, there is no pressing time on when you should update this.