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Now that you are married you have two options. You can file Married Filing Jointly (MFJ) (combined income and deductions) or you can each file Married Filing Separately (MFS). Most times, MFJ will provide the lowest tax liability. Also, if you choose MFS you must both claim the standard deduction or both itemize deductions. Additionally there are some special rules when you file MFS. See pages 6 & 7 of IRS Publication 501 (link below)
Regarding your child, only one of you can claim the child as a dependent.