Hi,
"I participated in the local running competition and came first" is correct
So is, "the first item on the agenda is ..., the second item on the agenda is..."
But firstly would NOT be correct in those sentences.
"Firstly" is only used to indicate that something is the first thing someone wants to say, for example:
"Firstly, I want to say that every performance was very impressive. But we have to choose a winner, and on this occasion it was ..."
"Firstly" is used to indicate that what you are about to say is the first thing, but there will be more things afterwards.
You can also use "secondly" to mark out the second thing, even if there is no third thing. Same for "thirdly". You DON'T hear "fourthly", "fifthly" or any subsequent "ly"s.