I work with clients every week who are moving into the area and they all are surprised at just how competitive the rental market is. If they see a house they like, they know they have to act on it quickly, especially if it is priced under $1300 per month.
When considering prospective tenants, property managers and landlords will review not only your current income but your credit history as well and criminal history if any. They want to make sure you are not only capable of paying rent but will pay the rent in line with your past payment history.
If you want more tips on what you need to know about renting a home, here's a link to my trulia blog
If you'd like some tips on improving your credit score, use the link below