If you are worried about an insurance rate increase, that should not apply when you are rear ended at a light.
It doesn't count against you in an accident where it is not your fault, regardless of which insurance pays.
You should not have to wait for a police report - Just call Progressive with the correct license number and they will get an adjuster out to assess the damage.
Fixing it yourself is a bad idea.
Your car needs quite a bit of work and parts.
If you start doing work yourself you could hose your chances for a full recovery.