@Kiara Moon There is always risks that A.) the tenants might damage the property, or B.) the tenants don't pay rent and won't leave. We must screen our tenant's thoughtfully and have a clear lease agreement. For this, LLs do background checks to see that people have been good renter's in the past and can afford to pay the rent on the first of every month. We collect security deposits to cover cleaning or damages that may arise out of the tenancy. Family members are no exception.
Renter's insurance covers the personal property of the tenant, not the building. Be sure you have enough property insurance. Let your agent know that you now rent the place and ask if your home owner's policy needs updating.
You can prohibit pets, they chew things, bend window blinds, disturb the neighbors and make wet spots if left unattended. Your lease might say, "Pets are not allowed on the property, including pet sitting. If a pet is found on the property, this is grounds for breaking the lease and Tenant will be given a three day notice to vacate. Tenant's security deposit would be forfeited."
Or, you can allow pets, "One dog or one can under 20 pounds is allowed. Tenant will pay a non-refundable deposit of $300 (or what ever you determine) on the day of lease signing. Tenant will pay monthly pet fee of $40 (or what ever you determine) at the same time as the regular rent" . . with the usual language of picking up the yard. Tenants must agree to pay for any damage caused by the pet.
If the interested people do not agree to your terms, you have saved yourself from a headache.