Don't assume you will owe less taxes because you are married. Unless one of you has an income that is much higher than the other one, you will owe the same or more. We hit the alternative minimum tax (AMT) as a couple although neither of us would hit it if we were single, so we pay more taxes because we are married. With the AMT, a lot of our deductions aren't allowed.
Also, whoever wrote earlier that you could file as Head of Household when you are married is wrong. You either have to file as married filing jointly, or married filing separately. The only way you can file as Head of Household if you are married is if you have been separated for the last six months of the year and you meet various other qualifications as well. Married filing separately is usually a bad deal unless one of you has a low income and lots of medical deductions and the other has a higher income. Because allowed medical deductions are based on a percentage of your income, occasionally it helps if they are high for one person to be married filing separately.
Here are the IRS rules on filing status (including who is eligible to file as Head of Household):
https://www.1040.com/federal-taxes/filing-basics/filing-status/