Which of the following characters should I choose to write an account about from To Kill a Mockingbird?I need to compose a first person narrative...

In order to select the character from To Kill a Mockingbird whose account you wish to write, return to the narrative of the trial and the comments of the characters around the time of the trial.  Find things that they have said before, during, and after the trial.  Probably, the character who has had the most to say during the trial--other than Scout--is Dill.

Since you know the feelings of Dill during the trial as he is sickened by the transpirings, you can base your account upon his feelings of sensitivity and what events have triggered his feelings. In Chapter 19, when Mr. Gilmer questions Tom Robinson and mocks him for saying that he felt sorry for Mayella, Dill begins to cry and Jem makes Scout take Dill outside.  Dill tells Scout that he does not care that other lawyers talk to Negroes like that; "Mr. Finch doesn't":

I don't care one speck. It ain't right, somehow it ain't right to do 'em that way.  Hasn't anybody got any business like that.--it just makes me sick.

Then, from behind a tree Mr. Dolphus Raymond commiserates with Dill,

You aren't thin-hided, it just makes you sick, doesn't it?

.Obviously discontent with the cross-examination and the verdict, Dill's case is fairly well outlined for the latter part of the trial.  All that is necessary are the initial feelings of Dill that can be based on his previous behaviors in the narrative.

Jem, too, is a good candidate since he becomes involved in the proceedings that precede the trial.  For instance, in Chapter 15 when men come to the house to speak with Atticus, Jem seeks to protect his father by yelling out that the phone is ringing so that Atticus will reenter the house.  And, since Jem is a little older than Scout, he can more easily follow the proceedings of the trial; he leans on the railing and listens intently.  Then, in Chapter 22, Scout narrates,

It was Jem's turn to cry.  His face was streaked with angry tears as we made our way through the cheerful crowd.  'It ain't right,' he muttered, all the way to the corner of the square where we found Atticus waiting....

When Jem repeats his statement to Atticus, his father agrees. Later, Jem asks his father, "How could they do it, how could they?"  Clearly, Jem has followed well the proceedings and has a sharp sense of what should follow logically from these proceedings. Thus writing an account from Jem's point of view would be rational and deductive with little emotional interpretation, although he feels strongly at the end of the trial after he hears the verdict.