A float shoe for a downhole tubular or casing includes a housing, a nose, a support, and a valve. The housing is attached to the casing, and the nose having a shell of a millable material (e.g., composite, aluminum, etc.) extends from the housing. A support of cement, fills an internal cavity of the nose's shell and support a valve in the housing. The shell for the nose defines a flow passage communicating with the valve and can have a conical or eccentric shape to facilitate passage of the float shoe in a borehole during run-in. The shell for the nose can also have a port or jet that communicate the flow passage out the side of the nose.