First is an adjective and “firstly” is an adverb (and the same can be said for “secondly”, etc.).
Adverbs say something about a verb. Here is an example: Mr. Rajoy quickly ran into the bar.
That is easy. What about these sentences?
- Firstly, Mr. Rajoy drank a beer.
- Secondly, he drank a glass of red wine.
Where are the verbs that are attached to the adverbs (for example, firstly)? There are none. An error. The correct form should be:
- First, Mr. Rajoy drank a beer. Second, he drank a glass of wine.
Words such as “first” are adjectives, in this case adjectives with elliptical (elíptico) nouns. The text could read: Mr. Rajoy´s first action was that he drank a beer. Here we have a sentence of ten words, compared to six words (First, Mr. Rajoy drank a beer).
On the basis that six words are better than ten words, we know which option to choose.