What points can you include in a letter from a commoner to Brutus in order to convince him he should be the ruler instead of Caesar?

I'm assuming the letter would be presented to Brutus before Caesar's assassination.

You could mention that Brutus, as a man of the people, would act for the people, unlike Caesar, who only seems to care about himself. 

Secondly, Brutus displays deeply entrenched values, whereas Caesar's morals seem to be suspect.

Also, Brutus does not display the kind of supercilious arrogance that seems to be an attribute of Caesar's character. Brutus comes across as humble and caring.

Fourthly, Brutus commands great respect among the common folk because of the above-named qualities, whereas Caesar generates skepticism and suspicion since he focuses only on his victories and thrives on adulation.

Furthermore, Brutus presents an image of courage and strength, whereas Caesar could come across as frail and infirm. Caesar is prone to fainting spells brought about by his supposed epilepsy, while Brutus is physically robust. It is easier to be inspired by a leader who presents an image of resilience and power than one who comes across as weak and unstable.

The general image of Brutus, therefore, much favors him as one suitable to lead, as Cassius so cleverly and slyly suggests during their speech in Act I, Scene 1.