You purchase renter's insurance if you are renting a house/apartment etc. and you want to protect your personal possessions (the stuff inside the building that you are renting) if they are damaged or stolen. Or if a guest in your home slips and gets hurt you would be covered.
Homeowners insurance provides financial protection against disasters. A standard policy insures the home itself and the things you keep in it.
Homeowners insurance is a package policy. This means that it covers both damage to your property and your liability or legal responsibility for any injuries and property damage you or members of your family cause to other people. This includes damage caused by household pets. Damage caused by most disasters is covered but there are exceptions. The most significant are damage caused by floods, earthquakes and poor maintenance. You must buy two separate policies for flood and earthquake coverage. Maintenance-related problems are the homeowners' responsibility.
Landlord insurance serves to protect landlords during circumstances where they are prevented from using their property to earn an income.
Your best bet is to call an insurance agent and ask them what type of insurance you would need to protect you from things like dog bites etc.