What information is required to determine the direction to a celestial object from a location on the Earth's surface with the best attainable a priori accuracy?

The position of date of the celestial object consistent with ICRF, the position of date of the observing point consistent with ITRF2000, the IAU 2000 precession/nutation model evaluated at the TT epoch, corrections to the celestial pole position, the terrestrial pole position and UT1 from the IERS interpolated to the epoch, and corrections for parallax, light time, aberration, refraction and telescope/antenna pointing corrections as necessary. It is not necessary to distinguish between geocentric and topocentric effects. Thus in the case of aberration, the velocity would be the combined effect of the Earth orbital motion and the site-dependent contribution from Earth rotation.