The Shulchan Aruch rules that only a garment made of either wool or linen is Biblically obligated in Tzitzis. Accordingly, one who wears a garment made of cotton, silk or other material, they are only fulfilling a Rabbinic obligation. This is the opinion of Rambam and Rif.
The Ram”o writes that the Halacha follows the opinion that garments of any material are Biblically obligated in Tzitzis. This is the opinion of Tosfos and the Rosh.
The Alter Rebbe writes that one who wants to fulfil the Mitzvah in the ideal way, should ensure that both their Tallis Gadol and Tallis Katan are made of white wool. The Mishna Berura writes that a G-d fearing individual should be stringent.
The Alter Rebbe writes that the garment and strings should be white wool. The reason for this is that the strings need to be of the same fabric as the corner of the garment. Rambam and Rashi rule that this requirement also refers to the colour of the strings, that they should be the same colour as the garment. The Mechaber in Shulchan Aruch rules like this opinion. The Ram”o writes that Ashkenazim will wear white strings even in coloured garment. The requirement that the strings be like the corner of the garment applies only to the material.
Whilst the Alter Rebbe rules that the Halacha follows the Ram”o, nonetheless he writes that one should wear a white Tallis Gadol and white Tallis Katan to fulfil the Mitzvah according to all opinions.
