I have 3,455 shares of my company stock options that I can exercise for an approximate profit of $39,000. I want to use a portion of this for debt, a portion for vacation and put the rest into savings. What's the best way to handle this to keep taxes as low as possible?

The exercise of stock options is typically treated as compensation, which means the company withholds the required income and FICA (Social Security and Medicare) taxes. This being the case, there is no specific tax savings strategy; the entire process is essentially OUT of your hands.