Hey, this has been bugging me too. After searching around it seems that comienza would be like commence in english and empieza would be like begins in english. In this was empieza is a little more casual and comienza is a little more formal, or at least that's how I'm interpreting its use.
In English, 'an' is used before words that start with a vowel sound and 'a' is used before words that begin with a consonant sound. It doesn't matter whether the word actually starts with a vowel or a consonant, the only important thing is the sound. The 'h' is silent in 'hour', so you must use 'an' and not 'a'.