What taxes are due at the the time of transfer and what taxes are due if the house is sold?

Assuming that your question concerns taxes upon the death of the original owner, that would depend on the state of residence at the time of their death and the size of their taxable estate. Assuming that there is no federal estate tax due and no state inheritance tax due, then the beneficiaries would have gain only if the property was sold. A beneficiary deed would not prevent a step-up in basis to the fair market value of the property on the date of death. So gain upon sale of the property should be calculated from the value on the date of death to the date of sale. This can be a complex area, so be sure to consult with an attorney who specializes in estate matters and a CPA who specializes in calculating capital gains.