" is it better to use tax assessment or fair market value?"
No, you can't do that. Your cost basis is the *LESSER* of what you paid for it, or the FMV at the time it was placed in service as a rental. Since this was gifted to you and you assume the giver's cost basis, there is no question that what the giver of the gift paid for it, is the lesser. The IRS specifically states that you can not use the tax assessment value, except under extreme circumstances. Your circumstances are not even anywhere close to extreme.
