Bad credit? This may help.
Most landlords and management companies want a minimum of 650 credit score, although they're looking for someone who has a credit score of 700 or above. Management companies are more strict and less flexible than independent landlords though. Another thing that might help is rent receipts that document on time payment, as well as good landlord references, if you have any.
You may end up needing a guarantor, though, and if so, know that most management companies want in state guarantors, however, there are some landlords who will accept out of state guarantors. Guarantor income is usually annual income 80x monthly rent, or in some cases, bank statements indicating sufficient liquidity to cover one years rent.
Many landlords will focus on the contents of the report in addition to the actual score. If your score is low (and 600 is low) because of repetitive failure to pay your bills rather than one or two items that relate to a particular account (maybe you are challenging some item) or event (medical bills) the landlord will likely conclude that you are not good a paying your bills and act accordingly.
For a better future it is important that you closely examine your credit report for accuracy (you are entitled to a free report from each of the 3 agencies one time per year - they will not give your credit score but it is the content that is important), challenge any errors (the closer to the time of the occurrence the better it is for you) and pay off any lingering minor issues that may be with a collection agency.
Moving forward, pay your bills on time (so many ruin their credit because of being late on a $20 credit card bill), maintain a good level of % credit available (do not max out any of your credit cards, spread your use over all your cards) and do not accept every credit card offer that comes you way. Congrats on your new job and enjoy NYC - it's a great town.
Flexibility in what you expect will really help you. You can always move out in a year to the apartment of your dreams, with a great reference letter from your NYC landlord in hand.