开始 (kāishǐ) is the most common, all-purpose word for 'to start' or 'the beginning' — you can use it for any activity, event, or time period. 开头 (kāitóu) is more specific, often referring to the very beginning of a story, speech, or process. 最初 (zuìchū) means 'at first, initially' and is used as an adverb or noun for the initial stage.