Because I grew up in Omaha, I was curious where in the city this zip code was located. I thought it might have been near UNO, the Med Center or Creighton, since you the focus was rentals.
I pulled the zip in city-data and found that 74% of the population rents in this zip. That's quite high. Also, the average age is younger. I have no specific rental history info to share, but thought you might find the stats from the city-data site helpful.
If you google Omaha rentals or Omaha homes for rent, there are several web sites with rentals.
If you want to purchase a home, you will need to consider how long you will be here to decide if that
is the best way to go. If you will only be here for 2-3 years, I recommend renting. I can send you a selection of homes if you wish to purchase.