Thank you for your question.
Almost everyone should either have Renters or Homeowners Insurance.
Since you are renting, than YES you should get renters insurance. A typical policy will cover for Personal Property Coverage, Liability Coverage, and possibly Loss of Use as well.
With Personal Property, consider requesting "Replacment Cost Coverage"
For Liability Coverage, get the most you can afford and a number that matches something near your net worth.
Make sure both of your names are on your policy. Tell your agent about any high value items that you may have.
And just for the record, many leases require you to have renters insurance.
Best of Luck to you and your new family.
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