Down payments for primary residence, conventional financing can be as little as 3%. It all depends on what loan programs you qualify for.
Debt to income ratio should be under 50%
Some lenders allow for 1 month rental history to count the income, again, depends on lender and loan program.
You should call a couple lenders to find out your options and create a plan from there.
any credit score over 740 doesn't really get you anything better.