Wool has always been the tallit fabric of choice from a halachic perspective, because, as the Shulchan Aruch notes, only a wool tallit or garment is required to have tzitzit. Since tzitzit is the raison d’etre of the tallit, wool is preferred because by wearing a wool tallit you fulfill the mitzvah of tzitzit d’oreisa (at the Torah Law level). A tallit made out of a different type of fabric – cotton, silk, etc. – only fulfills the mitzvah of tzitzit at the Rabbinical level.
However, the Rema, based on the Tosefos, rules that all types of material require tzitzit d’oreisa, and his ruling was accepted as the Ashkenazi custom. (This halachic dispute, by the way, is the reason why some Sephardim wear only wool tzitzit garments, even in summer.) Therefore, according to the Rema, a tallit made of silk or cotton is fine.
Lightweight Wool Tallit
From a practical standpoint as well, wool offers a number of advantages. It looks nice, hangs well, lasts well over time and resists stains. Many people break out in a sweat just hearing the word “wool” but from my experience, wool worn loosely is not any warmer than other fabric. A more pertinent question is how thick the fabric is and how well the weave breathes. For those who want a super lightweight tallit, I recommend the Kalil (a.k.a. Klilas Yofi) or the Tashbetz without a lining.