Are you writing an essay about the entire play?  If so, you may wish to select a theme and make a judgment about this theme or one of the motifs.  Your support will need to come from various acts of the play, of course.  For example, you may wish to examine how the motif of ambition is developed. For this thesis you can use Marc Antony's remark in his funeral oration as a motivator:  "Ambition should be made of sterner stuff."  For, this line is ironic since Brutus, and especially Cassius who is so ambitious are not of the "sternest stuff" and are defeated by Antony and Octavius.  Your thesis, then, can state that it is for his ambition that Brutus believes Caesar dangerous, but the conspirators prove to be even more ambitious and it is this ambition that is also their demise.

Click on the site below for ideas on themes of this play.

Or, perhaps you wish to analyze a character. There has always been great debate on who is the tragic character in this play.  But, many feel Brutus is, and you can glean some good ideas from the site below on this opinion.  So, for your thesis  you can state that Brutus is the tragic hero in "Julius Caesar" because he is of noble stature and has noble ideals, but he makes a tragic mistake for which he pays tragic consequences.