Low Credit Mortgage/FHA questions/ADVICE needed?

My boyfriend and I are wanting to purchase a house around $ 70,000. When I figure our income and dept to income ratio I come up with that we can afford a house over $ 110,000. (But we are set on the house at $ 70,000) However, I have very low credit (mistakes I made a few years ago, charge offs, collections, etc) I have a student loan in good standing and have never been late, but that’s about the only good thing. He has a auto loan, but the bank did not report his payment history for the first 10 months of it, so his length of having credit is fairly short, and that loan and a previous auto loan that was in perfect standing are the only thing on his credit report. His Experian score is 633, but we were told by a bank his median score is 593. That same bank wants us to pay $ 350 for the underwriting process. We are first time home buyers, so I just want to know what our options are. What is the possibility of finding a place to approve us? We will save a lot of money purchasing a home, compared to our high rent. I figured that in the past 5 years I alone have spent around $ 45,000 RENTING! Should we go through with the underwriting, should we try to contact a broker, should we wait? Any advice would be greatly appreciated.

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