I recommend searching on Trulia for the specific rental criteria you've mentioned.
To get you started, here are rentals in Denton under $900:
From there, you can add more criteria to narrow it down. Once you've got exactly what you want, you can even save the search (orange button in the upper left hand side of the search results page). That way, you'll get emails when new rentals that match your needs become available.
Hope that helps!
Trulia's Marketing Team