linen, cotton, shantung, and matka are particularly nice during spring-summer season when colors can also be lighter.
Standard silk ties are good year-round.
Wool, cashmere, and challis are great for fall-winter.
Silk neats (dots, floral, PoW, houndstooth, etc.) are the most formal style of ties and thus especially appropriate for suit get-ups.
Knits are great for more casual looks (odd jackets).