Many of the programs for first-time homebuyers were created to help with down payments. For instance, the main benefit of the HomeReady program is flexible underwriting guidelines, reduced mortgage insurance, and a minimum down payment of just 3 percent. You seem well-qualified and not in need of that help.
If you were my client, I'd ask about your monthly debts like auto loans, credit card balances, and student debt, and I'd want to know about your retirement savings. Because a well-qualified buyer with a good credit score like yours probably only needs to put 20 percent down to get approved for a prime loan at a good rate.
A bigger down payment is appropriate if you have no higher-interest debt, if you need a lower monthly payment for other reasons (supporting another relative, charitable contributions, or expensive hobbies, for instance), and if you can make that without sacrificing your emergency funds (which should cover at least three month's expenses for a wage-earner, and six for a self-employed pr commissioned individual.
Your choice of program depends on several things -- mostly your timeframe. If you intend to keep the home and its mortgage for only a few years, a 5/1 hybrid could have a rate .5 to 1 percent lower than that of a 30-year loan. If your goal is to keep the home for many years, a 30-year mortgage might be best. And if your goal is to become mortgage-free as soon as possible, you have two choices. One is to put the max down and get a 15-year loan, which comes with rates similar to those of 5/1 hybrids. The other choice is to take a 30-year loan, put 20 percent down, and start adding to your savings until you have enough to pay off the remaining mortgage balance. That can be safer, because if you need money, it's hard to get it back once you have paid it to a mortgage lender.
Finally, I'd say that with your good credit and large down payment, you're in a position to shop aggressively for the best interest rate. Make sure you get a few offers, and work with a competitive lender who can help you choose the right program.