first of all

1. 强调事物排列顺序，根据时间顺序依次列出一系列的动作，后面往往接next, then等。

First of all, you're supposed to indroduce yourself before speaking .

First of all, let me tell you the news. 首先，让我告诉你这个消息。

2. 最重要的是（= above all ）

German unity depends first of all on the German people.

德国的统一首先靠的是德国人民。

at first强调时间顺序，用于表示一段时间，常与稍后的一段时间作比较。(= to start / begin with / in the beginning)

At first he refused to accept any responsibility but he ended up apologizing.

最初他拒不承认有任何责任, 到头来还是道了歉.

At first, he was against our arrangement, but I managed to argue him round.

起初, 他反对我们的安排, 但我设法使他改变了看法。《简明英汉词典》