If you were able to get a loan, you'd be looking at a high interest rate. You didn't specify if 596 is your score and 603 is his. If one of you has a score higher than 603 you could apply for a mortgage individually rather than together. With a higher score, that would greatly increase your odds of approval.
That said, if you're both looking at scores around 603, I'd work on improving your credit first and saving up. If you can put 20% or more down, that's going to look a lot better to potential lenders.
Best of luck to both of you!
It depends. Does your landlord want to sell the house to you for that price? If so the question is can you qualify for a mortgage with your current income and credit score. The best person to ask this question is a mortgage banker or your local bank. Many of my clients have used Barb Harkins of Premier Residential Mortgage here in Allentown. If you want to send me an email I can reply with her phone and contact info. If you are comfortable paying your rent you should be able to handle a mortgage on a home in this price range.