When practicing Tai Chi, keep the head, neck, and back straight. The whole spine has to be aligned properly to facilitate the rise of energy to the top of the head, and to avoid excessive pressure on the lower back and the knees. The body should be relaxed and the head held up, as though suspended on a string.
It is important to keep the shoulders relaxed and to drop the elbows. Bending, stretching, and the opening and closing of joints should feel natural and un-strained.
Regarding eye movement, there is an old martial arts adage that says, "Wherever the hands go, the eyes go." Generally, the eyes follow the hands.