You made a good choice. Irving in a great place to live. Meanwhile, I should warn you that it gets hot there during the summer, very hot.
If you want to find the rental fast you need to go online. A great variety of rental platforms are available today. I personally like http://www.zillow.com/ and https://rentberry.com/. They contain a lot of listing in TX. The second one even allows to sign the lease with landlord online.