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what are your minimum payments
Are you w-2 employee or 1099 or self employed
What are expected taxes
What is job history
What is lowering FICO scores...Any recent lates, any BK oe past foreclosures?
The numbers seem to be OK, but more info is needed. Alot fo things can be fixed with 40K down. Although in your shoes, I would push to get 20% down to avoid MIP/PMI.
I don't think your scores are high enough to go conventional-I'm thinking you have to have a min of 680 with a 20% down payment, without 20% down you'd need to be in the 700's.
FHA may be possible but more downpayment won't help because you'll have to pay MIP for 5 years no matter how much you put down.