General rule of thumb is if the damage is more than $1000 need a police report. Try to get out of a body shop for less than $1000.
You can usually file your own report with the police. In Va. ALL accidents involving a commercial vehicle (taxi, rideshare, truck etc) must get a police report.

"No fault" does not mean the same thing everywhere. Some states it means everyone has to have insurance, some states it means if you have insurance you need an uninsured motorist rider. Some states it means that your insurance is responsible to pay for your damages regardless and then subrogate with the other party.