Process of renting out my first investment property

[Raghavendra Jakkani]

I am new investor and have one investment property. Its a single family house in dallas. I want to put it out for rent and bit nervous about the process. I want to give it a try to find a tenant myself. I have few questions about the process. I apologize ahead for the long post.

1. After posting on the zillow, do I show the property to only those tenants whose credit/criminal and other background checks out? or show the property to interested tenants and ask them to apply if they meet the criteria?

2. Does anyone has a checklist that they can share to talk to potential tenant before asking them to apply?

My list includes - last 2 years employment history and current employment [2 paystubs], criminal checks, eviction checks, No Pets, No smoking, tenant pays utilities, maintains landscape, no subleasing, bring own washer & dryer, 1 month security deposit and transfer of utilities before moving in, rental insurance, all occupants will be on lease, notice period of 2 months for termination, tenant references, No cosigners, no painting walls, late fee notice, any hoa fines should be paid by tenant, inspection of property at 3, 9 and 12 months.

Please let me know if I am missing anything.

3. Any other clues or observations to make to understand if the tenant is good?

4. Does zillow do all the required background checks for tenant screening or should I also look for any additional options?

5. If the tenant has a support animal, how to verify the validity of it?

6. If the prospective tenant has a realtor/agent, do I need to pay them?