Actually, they are grouped (I could be wrong here on this, just a pilot) as
-Hull insurence, damage to the aircraft
-Liability, for what you crash into
-Medical, for your passengers injuries
From what you say, then its your baby. You crash into something, you our your estate is responsable. Many companies provide what is known as "renter's insurence" which will, depending on your policy, cover who/what you crash into, damage to the aircraft you're flying, injuries to those on the ground.
This might be something to look into if you have assets worth protecting. In this day and age, its those with deep pockets that get sued. If they see you don't have insurence and have no assests, well, you can't get blood from a turnip now can you?
Happy contrails - I support B747Skipper and Jetguy