I don’t like to dither over style choices. At the beginning of a sentence, it’s routine to start the next word with a capital letter. But when I type a colon within a sentence, I often have to stop and think about how to write the next word: whether to cap it isn’t always obvious.
The Chicago Way
As I not-so-sneakily demonstrated above, Chicago style lowercases the first word after a colon within a sentence, even if the words after the colon are themselves a grammatically complete sentence (see CMOS 6.63):
They even relied on a chronological analogy: just as the Year II had overshadowed 1789, so the October Revolution had eclipsed that of February. [full sentence after the colon]
The watch came with a choice of three bands: stainless steel, plastic, or leather. [sentence fragment after the colon]
As always, there are exceptions.
