You are correct that a violent crime is one where a person or persons are injured or killed. So, battery, murder, rape, or yes, even arson like in your example where people are injured can all be considered violent.
Not everyone who commits a white collar crime will go to prison, but some obviously do. Thing of for example, Bernie M***, who ran a Ponzi scheme. His crime wasn't violent, but he stole millions of dollars and ruined lives, and is spending the rest of his life in prison, having been sentenced to decades. The same is true of Lou P**, who once managed groups like NSync and the Backstreet Boys, but also was running a Ponzi scheme. Perhaps if they had stolen less money and actually made restitution (something else a court likes to see) the court would have gone easier. Conversely, think of the couple yesterday who was convicted of stealing from their company and defrauding the government -the prosecutor actually recommended probation and that is what the judge gave them.
A judge can also order prison/jail time, but then "suspend" the sentence, so that you never serve the time unless you violate the terms of your probation, such as by committing another crime. If you did any time in jail -say, for example, you spent months in jail before you could bail out, a judge could also order you to serve ______ amount of time, credit you time served, and suspend the remainder of the sentence. Judges have a lot of power in other words.
Aside from restitution, letters as to your good character, you staying out of trouble while awaiting sentencing, a lack of criminal history, another thing that I know impresses judges is where (if applicable) people take steps to correct the issues that led them to commit their crime. For example, lots of people steal because they have drug problems, and they need money to pay for the drugs. If a defendant voluntary goes into AA/NA, seeks counseling, etc. and shows that they are trying to do better and address the underlying issue, it makes them look good.
And of course, as I'm sure your lawyer told you, judges like a person who takes responsibility for their crime at sentencing, whether found guilty or they plead guilty. Standing up before the court and admitting with sincerity that you did wrong and are truly sorry for what you did -and not just that you were caught - can work in your favor.
As to why the court is moving your case up, I couldn't really speculate. It could be something as simple as there is time on the court docket (e.g., perhaps the judge had a trial scheduled that ended early or resolved itself by a defendant changing their plea) so the calendar opened up.