初めて = for the first time ex: 初めて試験に合格した！！ 初めて is commonly used when you will do it or you've done for the first time. 初めに = first of all, in the beginning ex: 初めに、ひらがなを練習しましょう。 初めに is commonly used when you'd better do it first.

首先 hajimeni 第一次 hajimete