Shakespeare uses multiple writing techniques and naturally makes important decisions (choices) about how to begin his story. First, he chooses to begin with a street fight, an illustration of the basic situation--the feud between the Montague and the Capulet families. Next, we might add that he immediately uses puns, in particular sexual puns, to grab the attention of the groundlings in the audience. This takes the form of a series of jokes about "maiden-heads" (virginity, hymen), "able to stand" (erection), "I am a pretty piece of flesh" (well endowed), etc. Next, once the two groups of servants are about to commence quarreling (dueling in the street), Benvolio (a Montague) appears and tries to quell the violence--in keeping with the Prince's recent order that the families desist from such public fights. We should note that Benvolio's name comes from the Italian "bene" or "good." Benvolio uses his own sword to try to stop the servants from fighting, as shown in the editor's note, which we must always recall is not written by Shakespeare: "[Beats down their swords]" (Riverside Shakespeare). Now Tybalt enters the scene and immediately establishes his own character, in contrast to Benvolio's, as one who promotes the violence! Let me be clear that we are now discussing Shakespeare's use of "characterization" with both young gentlemen. First, Tybalt chides Benvolio for having his sword out and engaging with inferiors (servants), "What, art thous drawn among these heartless hinds? Turn thee, Benvolio, look upon thy death." (I.i.66) We again see Shakespeare's use of sexual puns according to the notes in the Riverside Shakespeare: "with punning sense 'female deer without a stag [hartless].'" The implication, of course, is that gentlemen fight gentlemen; servants fight servants; come fight with me, sir!
More characterization ensues: Benvolio tries to explain that he has only drawn his sword to "keep the peace" which leads to one of my own favorite lines in the play, and a masterpiece of characterization, Tybalt's reply: "What, drawn and talk of peace? I hate the word As I hate hell, all Montagues, and thee." Good lord! He hates the word "peace"! As much as he hates Hell itself, any Montague, and Benvolio in particular? How can you not want to fight him, unless you fear for your life in doing so? Now that the nobles are at it, for Benvolio is indeed forced to fight, the conflict immediately escalates as Capulet and Montague themselves arrive on the scene and enter the fray with drawn swords. This battle is interrupted by the arrival of the Prince, who sets up the basic conflict which will drive the rest of the action--that any further public battles between the families will result in the penalty of death. Romeo will fall under this sentence, or nearly do so, later in the play when he kills Tybalt in vengeance for having killed Mercutio, although the sentence is mitigated to banishment rather than death.
The remainder of Act I, scene 1, establishes the character of Romeo as Shakespeare wishes him to appear before he meets Juliet. Shakespeare's first decision is to have Romeo spoken of by other characters, namely his mother, father, and Benvolio before we meet Romeo for ourselves. We learn that he has been acting oddly, going out before dawn to the woods to be alone, but coming back before sunrise to shut himself up in his room, and we learn that no one knows why he is acting in this manner. Benvolio sees Romeo approach and offers to find out what is troubling him--and thus we learn about Romeo's unrequited crush upon the lovely but as yet unnamed Rosaline. I have written of this crush elsewhere on eNotes, but should stress here that Shakespeare is attempting to show that Romeo has not the slightest idea what true love is, that this blighting crush is entirely a creation of his own mind, a projection of perfection. We are meant to contrast this shallow, false notion of love with the genuine article once Romeo meets Juliet!