There are two books you should check out on the topic of the audiences in Shakespeare's day.
Playgoing in Shakespeare's London by Andrew Gurr
Shakespeare's Professional Career by Peter Thomson
Your library is likely to have both copies. Both texts offer a complete breakdown of who attended the Globe and the different make-ups of audiences during different performances and dates.
There was a wide cross-section of people who attended Shakespeare's plays at the Globe
Royalty came and sat in the best seats, of course. Others of the business class (merchants,etc.) came and paid for seating. Finally, in the center of the horseshoe-shaped Globe Theater, stood what were known as the groundlings. These people were rowdy, often shouting and trying to interact with the actors. They would even throw rotten vegetables if they thought the play were bad. This behavior is much like that of some viewers of vaudeville acts in the United States in the early 1900's (1915-1930 or so).
The groundlings desired action and ribald jokes. However, while the aristocracy also enjoyed the actions and puns, they delighted in the beauty of the language and poetic devices that Shakespeare employed. For example, in Romeo and Juliet, the aristocracy enjoyed greatly the light/dark imagery and the two sonnets incorporated into the blank verse (unrhymed iambic pentameter) of the play.
There is very little actual evidence about the Globe's audience, or in fact about playgoing at all in Shakespeare's day. We know that the theatre in Bankside, London was in a salubrious area of the city, and fought for customers against bear-baitings and whorehouses - quite different from the comfortable, cushioned middle-class audience associated primarily with theatre today.
Though the different tiers of seating (from standing positions in the yard right up to comfortable seats up in the gallery) seem to indicate a huge variety of theatregoers, from right across the class spectrum, it seems that the theatre was primarily thought of as a popular, rather than an elitist, art. Today, of course, television is the "popular" entertainment, and theatre is for those who can afford it.
We know that the Globe held about 1000 people at a time when London's population was around 300,000. So in 300 sold-out performances, the whole city would have seen the play - obviously, this would never have happened, but it makes the point that the theatre was the popular entertainment of its day.
As for how they acted, we just don't know. Some scholars think that the audience would have shouted, eaten throughout the performance, and thrown things at the stage (booing the French, for example, in "Henry V"). Some think the audience would have been quiet like audiences today. There really isn't any solid evidence.
There was a film a few years ago called 'Shakespeare in Love'. It's a great film about Shakespeare and many scenes are filmed in the original Globe Theatre (they have rebuilt The Globe exactly as it was in Shakespeare's day).
Much of the film concerns Shakespeare and his players staging the original performance of Romeo and Juliet. The last half hour of the film centers around the opening show, in a packed out 1590s Globe Theatre.
The film was written and produced by Tom Stoppard, a Shakespearean academic and theatre expert. The film presents the best idea we have of what it would have been like.
(And it's a GREAT film!) If you can find a copy, it will answer your question.