From this ELU post first answer, it is said that:
Eric Partridge ("Usage and Abusage") says:
firstly is traditionally said to be inferior to first, even when secondly, thirdly ... follow it.
As many others have mentioned, both are perfectly fine. Additionally "firstly" is more formal than "first" to most. Another ELL answer on that can be found on it (add on @Dongrui_Yang's answer).
Some alternatives are found here:
firstly = first off / "for a start..."
secondly = next / and then / another thing
moreover/furthermore = on top of that/this
It is said by Grammarist that:
“Firstly,” “secondly,” and “thirdly” are superfluous terms. “First,” “second,” and “third” are more acceptable words for enumerating text in writing. Experts also prefer “first” even if the other items state “secondly” and “thirdly.”
It is also said from Merriam-Webster that:
In writing, first is much more common than firstly and is probably the best bet for most situations, even if the only reason is that a reader may wonder if firstly is proper and be distracted by this word choice.