Which movement style is typically quicker and often characterized by lively rhythms?

The movement style that is typically quicker and characterized by lively rhythms is indeed allegro. This term indicates a fast, lively tempo, often bringing a sense of joy and energy to the music. In classical music, allegro sections are usually contrasted with slower movements, creating dynamic shifts within the piece.

Adagio, which suggests a slow tempo, creates a more contemplative and lyrical atmosphere. Moderato indicates a moderate speed, neither fast nor slow, providing balance but lacking the vivacity of allegro. Lento also implies a very slow tempo, emphasizing a different mood entirely. Thus, allegro stands out for its quick pace and lively character, making it the correct choice in this context.