During the week I wear a T shirt every day for work. On Shabbat I wear a white shirt. Is there a reason specifically that I should wear a white shirt? As long as I have special shirts for Shabbat, is there a problem if the shirt is coloured?
There is no problem with the shirt being coloured, provided it is special for Shabbat. By wearing a special shirt for Shabbat you fulfill the instruction of ensuring that your Shabbat clothes are distinct from your weekday clothes.
However, if your community all wear white shirts, it is preferable to do so, too (at least for going to shul etc.), because this is the “communal” way of honouring Shabbat, and wearing a coloured shirt might be giving a “weekday” impression. This depends on how universal the custom of wearing a white shirt is in the community.
Based on Kabbalah sources, some have the custom of wearing “all white” on Shabbat, but this generally not customary (among non-kabbalists).