What is the minimum credit score accepted to get a mortgage? And how long I need to be paid with checks?

I am trying to buy a condo. Nothing fancy, my maximum is 50K and I will put about 10k down and I was looking for a 15 or 30 year fixed rate. My credit score is about 680 and I have been working with checks for almost a year now. I make about 45K a year. I never made a late payment on anything. My credit history is just fresh but not destroyed and rebuilt. Do you think I have a chance?

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