There is no such word as “firstly.”
— Sherwin Cody, How to Do Business by Letter, 1918
A number of 19th century usage guides cautioned against the use of firstly (“in the first place”) on the grounds that it was a pedantic neologism, when the word had in fact been in use since the 14th century. More recent complaints tend to recommend against the word on the grounds that first is shorter, or because it is seen as preferable to have consistency when writing a list such as first, second, third, etc. You may choose not to use it if you wish, but saying that it is not a word is contradicted by significant evidence of use.
There are two Propositions, which are the Objects of our Attention. Firstly; The Protection and maintaining of our Property. And, Secondly; to use the greatest care and Prudence, not to break the Articles of Publick Faith, or insult Governmental Authority.
— Ethan Allen, A Brief Narrative of the Proceedings of the Government of New York, 1774