The classic color of a Tallit is white. What is the Halacha regarding a colorful Tallit Katan or Gadol? Interestingly, the Shulhan Aruch (Siman 9), based on Rambam, states that the color of the Sisit strings should match the color of the Tallit. This is either because of "Zeh Keli V’anvehu," enhancing the beauty of the Misva, or because it is derived from the Pasuk, "Al Kanfeh Bigdehem," (on the corner of their garment) from which Chazal derive that the fringe should be the same type and color as the corner of the garment. While the Ashkenazim hold that white strings are Halachically compatible with any color Tallit, Maran rules that the color of the strings should match the Tallit.
Accordingly, the Chesed L’Alaphim )R. Eliezer Papo, Bulgaria, 1786-1827) holds that ideally one should wear a totally white Tallit with white strings to avoid any problems. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) in Parashat Noach discusses Tallitot with stripes of other colors and rules that it is permitted because the majority of the garment is white. This is unusual, because generally, the Ben Ish Hai follows the ruling of the Chesed L’Alaphim. The commentators explain that he was lenient because when he came to Bagdad he found the community already wearing black or colored striped Tallitot, and therefore, he was "Melamed Zechut"-justified their practice, after the fact.
Therefore, people who buy "technicolor" Tallitot, thinking that it is a "Hidur" enhancement of the Misva, are actually not following Maran, because the white strings on a colored Tallit are not Lechatehila (ideal). The same applies to the Tallit Katan issued by the Israeli Army. They made it in olive drab, but according to Maran, it would also require green Sisit.
The Torah recognizes two materials as being obligated in Sisit: wool and linen. The Rabbenu Tam in the Tosafot in Masechet Menachot asks why it is not common practice to make a Tallit out of linen. It would seem to be a lightweight comfortable material, ideal for hot weather. He answers that a linen garment poses a potential problem of Shatnez, the prohibition of weaving wool and linen together. In the times when there was Techelet, the blue dyed wool strings, it was permissible to attach them to a linen garment, because the Misva of Sisit overrides the prohibition of Shatnez. Nevertheless, there was a Rabbinic enactment to refrain from using a linen Tallit out of concern that someone may wear such a Tallit at night, when the Misva of Sisit is not in effect and thus violate Shatnez. Although nowadays we do not have Techelet, and one could attach Sisit of linen, the enactment is still in effect. The Rambam argues and says that it is permitted to wear a linen Tallit with linen strings. Maran says that although technically the Halacha is like the Rambam, one should follow the Tosafot and not use a linen Tallit. The Rema points out that it is better to wear a linen Tallit with linen strings than to wear no Tallit at all. Nowadays, it is a prohibition of Shatnez to attach wool strings to a linen Tallit. Sisit only overrides Shatnez when the Techelet strings are present.
The color of the Sisit should match the color of the tallit. Therefore, one should try to use a white Tallit.
One should not wear a Tallit made of linen, even if he uses linen strings.