Good morning, Jon....
If you are not a Veteran, than an FHA loan with a minimum of 3.5% down is possible. However, you are required by FHA to buy a primary residence. A 2nd home is defined as a vacation home and is different from a primary residence. If your purchase is truly a 2nd home, you are looking at Fannie or Freddie which, depending on the area, may require 5-10% down with MI. To rid yourself of the MI, you would be required to put 20% down.
John's list of questions are key to giving you a more accurate response! Nice job, John!