Here are the elements to get you the best interest rate: a) FICO 740 or above, b) Debt to Income (DTI) less than 50%, c) no derogatory items on your credit report, d) being a full-time employee in the same line of work with no gaps for at least 2 years with stable or increasing annual income.
There are loan products that allow as little as 3% down for first time home buyers. As mentioned before, mortgage insurance (MI or PMI) is required (either borrower paid or lender paid) for loan to values (LTV) greater than 80%, typically. If PMI is lender paid, it results in a slightly higher interest rate but you do not see an actually monthly line item for that cost; it also means you pay for it the entire term of the loan rather than being able to cancel PMI once your LTV reaches 78% of the initial purchase price.
Keep in mind that on top of a down payment you will have other closing costs and fees to cover, such as: appraisal, home inspections, title, escrow reserves, pre-pays for home insurance and interest. If the home you are looking at has mandatory HOA dues, those will need to be factored in to your overall monthly payment too.
Don't think you are looking for the home you will retire in as your first home purchase. You are looking for a starter home to stay in less than 10 years, typically. Good luck!
Step 2 is flawed logic. Make excess principal payments on your highest interest rate loans first. This will result in the fastest paydown of outstanding debt as it will reduce interest costs.