I've used a lot of the companies listed below, but have not been satisfied. Either too difficult, too costly, or just not friendly.
Last year I switched to TenantMagic and have to say I am much more satisfied. Actually designed for landlords like you and me.
Free to use, excellent customer service (I called number listed and got in touch with owner in seconds), and much simpler than anything I've used before.
Best tenant screening company is TenantMagic.