FHA requires 3.5% down, but it can be gift funds from a relative. USDA offers 0 down, but there are restrictions as to where the property may be, it's targeted to rural areas. The rates are all pretty competitive, in the low 4% range. You'll have to meet with a local lender to be qualified and quoted the rates for the program you choose.
You say your DTI is around 33%, how did you calculate this? A lender will only use your credit obligations, like credit cards, car loans and the new mortgage. If this is how you did it, you may not have much to work with as most lenders will cap out at 45% combined. You may find that if you pay down or off some debt you'll both improve the credit scores and your buying capacity. Talk to a local lender to get a more complete picture of what may be possible. Best of luck.