I have owned rental houses since 1979 and still have seven. My best advice is to get an agent to handle rental applications. The agent will verify employment and income and check credit references, etc. They can advise you on the rental market and help you set a fair rent amount. The money you pay him/her (typically one month's rent) will be money well spent -- and it's deductible as I will explain below. The agent will get the tenants (and you as landlord) to sign the lease. That will offer some protection for you in case anything goes wrong.
Also contact your tax advisor. Renting the property will change it to an income property and you will file a Schedule E with your return next year. There are huge advantages to converting a property to a rental -- 1. you get to depreciate it (something you cannot do with your residence) and 2. practically every penny you spend on it will be tax deductible, except the principal on any mortgage on the property. Your tax person can explain the details.
In all my experience (35 years times an average of six or seven houses each year,) I have only ever had one case of intentional damage to the property and one eviction. PM me if I can be of further help.