There used to be a grammarians' rule that you must not write firstly; your enumeration must be: first, secondly, thirdly. It was one of those arbitrary rules whose observance was supposed by a certain class of purist to be a hall-mark of correct writing. This rule, unlike many of the sort, had not even logic on its side. Of late years there has been a rebellion against these rules, and I do not think that any contemporary grammarian will mind much whether you say first or firstly.