What do you get to know about Beatrice From Act 1, Scene 1?

In Act 1, Scene 1 of Shakespeare's Much Ado About Nothing, we learn a few things about Beatrice: she has an adversarial relationship with Benedick, she is clever and witty, she doesn't fully accept Elizabethan gender roles, and she is quite beautiful.
Beatrice's very first line is as follows:

I pray you, is Signor Montanto returned from the wars or
no?

A Montanto is an upward thrust in fencing—an unnecessarily flashy move that a real soldier wouldn't use. The reference displays her intelligence, since she knows the jargon of a traditionally male sport. It also demonstrates her familiarity with, and disdain for, Benedick, who she implies is all show and no substance.
 
She reaffirms this impression a few lines later, when she states that


For indeed I promised
to eat all of his killing.


In other words, she thought so little of Benedick's martial prowess, and she was so certain that he would not manage a single kill, that she promised to eat anyone he actually slew!
 
All of these impressions are reaffirmed when Benedick arrives in the company of Claudio and Don Pedro. Benedick and Beatrice engage in a war of words that lasts several pages. But after most of the cast exits, leaving Claudio and Benedick alone, we get this little gem:

There’s [Beatrice], an she were not possessed with a fury,
exceeds [Hero] as much in beauty as the first of May doth the last of December.


Benedick thinks Beatrice is beautiful—the first explicit acknowledgement of the flirtatious subtext of their arguments.