We have some etymological background from the accepted answer to a related question here. However, this question asks about understanding the word based on its history of first usage in New Testament literature, not the etymological or lexical meanings developed later through Church history.
Given that etymological background, there is no basis we can objectively define the word by because the word was created similarly to how Paul created the word θεόπνευστος (theopneustos).
2 Tim 3:16 (NASB)
All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness;
2 Tim 3:16 (Greek)
πᾶσα γραφὴ θεόπνευστος καὶ ὠφέλιμος πρὸς διδασκαλίαν, πρὸς ἐλεγμόν, πρὸς ἐπανόρθωσιν, πρὸς παιδείαν τὴν ἐν δικαιοσύνῃ,
When we examine created words like this, consulting experts only reviews their experienced guess; it's not objective.
Likely meaning from the historical setting
This created word has an obvious meaning: It uses the term "Christ" as a root with a suffix meaning "belonging to", with specific connotation of a slave-master relationship, albeit that Jesus was known as a good master. It's meaning was intended to be somewhat self-evident.
The term "Christ" means "messiah" and was known to be a title referencing Jesus at the time. This could have deeper ramifications for later study, that the Christians at Antioch (Acts 11:26) saw themselves as belonging to the messiah, specifically that Jesus was the messiah. Christians believe that the messiah has already come, while other religions may still be waiting for the messiah. But, that touches on another topic beyond the scope of hermeneutics. Nonetheless, the meaning of the word does have such implications.
The fact that Agrippa used the term (Acts 26:28) establishes a kind of government recognition that the term isn't just some fringe term that didn't matter.
Meaning based on usage
The New Testament Church was well-connected. So, Peter's usage would have been very much in tune with with what the Church at Antioch understood.
Bear in mind, Luke explains in Acts 11 that this was a new term and where the term originated. That is a good narrative introduction. Later, King Agrippa uses it. Now, Peter does also.
Peter's use agrees and elaborates further.
Ramifications of the meaning
The term isn't defined by any New Testament literature, meaning it is a useful label to describe what people already understood.
So, the most clear definition would be: The people told about through entire Book of Acts.
In a literary interpretation method (hermeneutics), we could say that the word "Christian" is the main character of the Book of Acts. The collective "Christians" are dynamic, they change and learn, face challenges, overcome, continue after the story ends. We could make a similar argument, for example, that through all Star Trek series, the main character is the transporter device because it changes as a dynamic character and affects all other things. That may be a stretch for some people to imagine, but such ways of examining literature are at the heart of hermeneutics.
The Church is the main character in the Book of Acts, while Jesus is the main character in the Gospels. So, the term "Christian" is being defined as this main character in Acts: the Church.
Peter also uses the term as if everyone already knows its meaning. So, it is not exclusively used or defined by Luke; Luke merely records as a reporter how everyone else was already using the term.
Therefore, in Acts, we don't exactly get "Luke's" definition; we get everyone's definition, both the Church and the king's.
So, by cross-reference, we could examine the final statement of Mark.
Mark 16:17-18 (NASB)
17 These signs will accompany those who have believed: in My name they will cast out demons, they will speak with new tongues; 18 they will pick up serpents, and if they drink any deadly poison, it will not hurt them; they will lay hands on the sick, and they will recover.”
That doesn't limit the meaning, but it contributes to it and it agrees with some of the less mistakable events Luke records in Acts. Though, it is very brief and can't describe it all. A more thorough definition would need an entire book, which Luke wrote in the form of Acts.
What we know about Christians from Acts and Peter consistently
They belong to Jesus. (etymological)
They believe the Messiah already came. (etymological)
They are the new type of people that began to flourish and increase in number and face challenges and overcome et cetera after Jesus ascended. (based on usage)
What we don't know
We don't get anything like:
I say, this is what a Christian is, so start conforming...
This is what it means to be a Christian in my view...
We don't get any like that, supplying any sort of definition or any sort of obligation or matter of differing perspective.
What we do know for sure
The New Testament definition of Christian was universal and went without needing to be stated because it embodied the obvious life and lifestyle of the people it named.