It is difficult to find knitwear to wear over a shirt and under a jacket because most of what is out there is less than ideal. For one thing, proper knitwear should be relatively light lest the wearer be overly warm indoors. Single ply is best, and certainly no more than two ply. For another, it should be sleeveless for the same reason (like a vest, the sweater is to keep the torso warm and add some additional color and texture to the ensemble). That leaves us with three choices, the vee neck, the cardigan and the crew, only two of them ever seen.
The crew is not a practical choice as to my knowledge no-one on this earth makes a sleeveless version even though there would be a nice market for them. For the closed neck would let men go tieless if they so chose, and many men would.
Whether four in hand, bow tie or ascot, both the cardigan and the vee neck really require silk to finish the look of the neck. Open collars and jackets are less than ideal, George Clooney notwithstanding. The best designs have a deeper vee, keeping the body warm but displaying an ample amount of necktie.
Within these limitations a variety of materials will do. Cashmere is wonderful of course, as are the modern combinations of silk, linen and wool in various proportions, alpaca and merino. Just avoid sleeves if you can.