Here is another update, based on the above discussions, I am summing up the suggested checklist (with no order)
• Verify your information in your naturalization certificate, check for any spelling errors or missing data.
• Sign your naturalization certificate.
• Update your status record with SSA, your naturalization certificate or passport will be needed, to be done in person. Some responders viewed this as optional.
• Update your status record with DMV, your naturalization certificate or passport will be needed, to be done in person. Some responders viewed this as optional.
• Register to vote, many debated this... After all, it a personal choice to vote or not... however it is highly encouraged.
• Apply for US passport (book), your original naturalization certificate will be needed. Based on the views, it is almost a requirement for your citizenship proof, or at least an uncomplicated method to proof. It is required for traveling
• Apply for US passport card (optional), your naturalization certificate will be needed.
• Update your employment status, file I-9 documentation with HR (optional), a debatable option, only your passport can be used.