The Proposed Statement
Once you file the Notice of Appeal, you have 15 days to file your Proposed Statement. Do not expect an extension on this date.
As a rule, you cannot introduce new evidence in an appeal. You are appealing the decision which the judge made based on the evidence available to the court at the time of the trial. The higher court will base their decision on a record of what has happened in the case (i.e., the Engrossed Statement), the written arguments (i.e., the Briefs) and the oral arguments (optional for you and the Plaintiff/Respondent).
The Engrossed Statement begins when you prepare a Proposed Statement and submit it to the lower court. Since this is the record of facts the higher court will refer to, it is important to include the factual support for the grounds of your appeal in the statement. However, remember that the judge and the DA (or City Attorney) also have to sign off on the statement. A statement which sticks strictly to facts and avoids any inflamatory remarks or interpretaion stands a much better chance of getting all of the parties to sign it.
The simplest and usually best way to handle the factual part of the Statement (when available) is to stipulate to the docket and the transcript as being the record. The judge and DA should agree to this without any argument.
The other thing required in the Proposed Statement is the grounds for your appeal.
Given all of the above, it makes sense to at least have an outline of your Opening Brief before you prepare the Proposed Statement. See why I recommended using part of the 30 days Notice of Appeal period for research?
Having prepared and submitted your Proposed Statement in a timely manner, your next step is the Settled Statement Hearing.