Someone may correct me, but based on my experience you must file either married filing separately or married filing joint (which requires reporting your spouse's income, which you likely do not want to do).
Your were married at the end of the year, therefore you cannot file as single. As I understand it, you can only file head of household if you are unmarried, paid more than 50% of the cost of keeping a home, and have a qualifying person living with you.
In order to claim an exemption for a NRA spouse, the spouse must have an ITIN, have no US taxable income and not be claimed as a dependent of another US taxpayer. Years ago you could write "NRA" on the line that asks for a SSN, but that changed a couple of years back.