Cambridge Grammar of English Hardback with cd-rom a comprehensive Guide

First(ly) and at first

First

or (more formally) firstly, not at first, is used to label the first item or point in a list:

In this paper we 

firstly review the empirical studies carried out by Annett. We then

discuss the ways in which genotypes are identified within the Annett studies, we

show that this is inefficient, and then describe a more powerful and sensitive method

that we use in our own empirical study.

At first 

is used to contrast two different situations in time:

Employment had 

at first been only too full, and the economy was overloaded. But by

the end of the period the very idea of full employment seemed illusory and even

Keynes’ view that 5 per cent was a reasonable level to aim for would have seemed

highly optimistic.