Can I get a mortgage with bad credit?

can I get a mortgage with "fair credit" score in the 620's last time I checked if I have half the purchase price as a down payment. All credit is 7 yrs or older so a lot of it will start falling off soon if I were to re-pay or try and repair my credit right now it would hurt me not help me because that would reset the dates and it would be another 7 yrs before it comes off . Plus paying it now is not going to make me look good because it has been so long too. I am finally back on my feet after a layoff completely destroyed my life and I lost everything. I want to buy a home and be done with credit forever because I never want to be in the position I was in before. That is why I want to pay half of the purchase price up front and only get a $25000 loan for the remainder with a 15 yr mortgage. Is this possible with my low score? if so does anyone know how?