tough situation.
You can always file jointly as long as your spouse agrees, even if your spouse does not work or is incarcerated. Joint filing almost always has the lowest tax or largest refund.
MFS is certainly an option. The main reason to file MFS would be either, your spouse does not want to file jointly; or, you think there is some financial shenanigans in your spouse's history. When you file jointly, you become jointly liable for all the facts on the return and any monies owed. You are presumed to be "in it together", whatever "it" happens to be, and the IRS can come after you for any money owed even if you allege the problem was caused by your spouse. Filing separately makes you only responsible for your own income and tax items. You will have to review your situation to see if that is a concern.
Lastly, I have some concerns about HOH. To file HOH, you must have a qualifying person. In your case, a dependent parent is a qualifying person for HOH even if they don't live in your home. But you must also be "considered unmarried" by living apart from your spouse. While this is certainly true for you at a basic level, the IRS considers incarceration to be a "temporary absence" and your spouse is treated as living with you even if they are temporarily absent, so your are not "living apart" for HOH status. However, the IRS also says "It must be reasonable to assume the absent person will return to the home after the temporary absence." I think you can certainly make a case that a life term makes the absence more than temporary, meaning you are living apart under the meaning of the HOH rules. But if you are audited, the IRS might interpret things differently.
So bottom line, MFJ is best, if you both agree. HOH is an option that will pay less tax than MFS. MFS is the last default if you can't or don't want to file as MFJ or HOH.
