Your home owner's insurance might not cover damages caused by your renters. My advice would be to go to your insurance agent and discuss the parameters of your policy. Your agent might be able to make some suggestions regarding renting your home and what kind of insurance features you should get. If you allow a person with a dog to rent the home, then charge them a deposit in case any pet-related damages occur. You could also suggest that the person occupying the home get renter's insurance for themselves. If they provide you with proof of insurance, you could offer a decrease in rent to cover those premiums. This gives you both incentives to have an adequate amount of insurance and coverage. Also, make sure that your initial deposit charged to the renter is enough to cover any damages that can occur from neglect or abuse.

I have rented for all my life and I have pets, so don't be biased against pet owners. You should just evaluate if they are good pet owners. Some messes are inevitable, but they likely will not destroy your house! My dogs have had maybe 2 accidents in my last home. Also, older dogs they usually are pretty mild and don't chew on things anymore. I guess you may want to steer clear of people with puppies. I would be more worried about kids than pets though, a friend of mine once visited and her 1 year old toddler threw toys and dented the walls. The toddler spat up everywhere also. It seems a toddler would be worse than a pet.

I rented a house to a family with two kids and a cat, and the cat peed in the corner and ruined the floor. The homeowner's insurance didn't pay anything so I just did not give back their deposit.