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I am looking into buying a house since I have about 20/30,000 in down payment money. I receive 1500 monthly. My Fico scores are 621 Experian, 566 Equifax, 617 Transunion. I am looking into either applying for a PHFA Mortgage or Trying with Quicken Loans for a FHA mortagage which would be better and what are the chances it would be approved.
You should be eligible for an FHA loan but to be quite frank you might want to look at the reasons why your credit score is on the 'lower' side of the 600 range and work towards building it in the short run. It may only require a few behavioural changes to your monthly credit management/spending habit and a month to wait for the creditors data to be reflected in your future reports and scores.
I'd recommend talking to a local lender who can provide you with a free mortgage credit analysis as this would be worth it's weight in gold.
Congrats on your decision to buy a home and good luck.