Any major airline will fly to Maui. However, only certain airlines will take you to Maui on a direct, nonstop flight. If you want to fly to Maui quickly and comfortably, find an airline with this option.
However, if money is not an issue, rent a private airplane. This will allow you and your group to fly in your own miniature paradise where the only passengers the flight crew has to dote on is you. You will be able to sit back and relax in luxurious comfort before arriving at the island. The private jet is certainly the fastest and classiest way to fly, though a first class ticket on a nonstop flight to Maui is a very close second.
If you are unable to find an airline that has a nonstop flight, find one with a single, short stop-over, usually in Los Angeles or Honolulu. Then, be sure to book a first class ticket for both legs of the trip to ensure utmost comfort and amenities. Though getting on and off an airplane in inconvenient, the benefit of first class is that you will board first and exit first, which is a huge time saver and much less stressful than waiting at the back of the airplane. This way, when you arrive in Maui, you will be first to experience the Aloha spirit and receive a beautiful flower lei to begin your stay.
Business class may as well be in the same league as first class, though the ticket prices are usually less expensive. Business class passengers receive the same treatment as those in first class--the only difference is that you sit closer to the cabin containing standard fare passengers. As long as you do not mind sharing the bathroom with those in the first few rows of the standard fare seats, business class is an excellent option. Now, if you happen to find an airline that can take you directly to Maui, that is just icing on your trip to the tropical paradise.