Hon, i have worked in the past in a number of real estate and have been myself a renter for the last 7 or 8 years.
I treat rental house hunting as i would a job interview. If i'm in contact with a real estate staff person i always make sure i am dressed very nicely and if i want to place an application i have it all filled out correctly before i walk back into their office. It always comes across as more professional then sitting in their office thinking over all the information, making calls, spilling paperwork everywhere.
Oh, i also make copies of all proof that i need and DON'T ask them to do it. Once again, shows you're responsible, professional and they love that you're not making them do a hundred copies of things.
I have NEVER failed doing this. If there's something i really want, i treat it as a job i want and give it 200%! When you're competing against several other people make sure YOU are the one that stands out in the crowd.
Hope this helps and good luck.