Regarding the original question, regardless of what swing you use...think about where your body is positioned at the top of the back swing and where your muscles are at impact. These are some of the muscles that help take you from a starting point (where you are going 0 mph at the top of your back swing) to whatever your swing speed is at impact. The faster you can go, the farther you'll hit the ball (many amateurs swing around 70-95 mph, many pros swing around 105-130 mph, and the top long ballers can swing 135 to over 150mph).
For me in particular as a right-hander and with my swing-style, some of these downswing muscles are:
Inside of my left forearm
Outside of right forearm
Right triceps
Right chest
Right obliques
Left quad
Left adductor
Right abductor
Right hamstring
Doing exercises to strengthen these muscle groups will help out quite a bit. It was mentioned to stay away from bench presses, but I think they are fine because they work your chest and triceps. But regardless of the exercise, be careful how you train. You can certainly add muscle, mass, and strength...but if you are training slowly you will be building slow-twitch muscle fibers and may actually slow your swing down. To get fast, train fast.
Some of the other posts here are good too.
Golf fitness has become really popular in recent years, but being fast and fit are two different things. You can be the great shape and not hit the ball far at all, and you can have a big ol' spare tire around your belly and crush the ball.
Don't sacrifice swinging fast at the expense of good contact. You can lose 20 yards on your drive by missing the sweet spot as little as 1/2 an inch.
And getting your equipment custom-fit and possibly going with a shorter driver to make good contact are good thoughts. I've hit two drivers that looked very similar but were different in loft, weight, length, shaft flex, and I literally hit one 50 yards further than the other.
Hmmm...although I DO advocate and enjoy flexibility and stretching, I don't agree that flexibility is absolutely necessary to hit the ball a mile. Neither Sean Fister (a Remax World Long Drive Champion) or JB Holmes (PGA Tour) swing to parallel...and they have plenty of distance.
And I have mixed feelings about heavy clubs. While they can help your golf swing strength, if you train slow with them you may be getting stronger but slower. Like I mentioned above, to get fast you must train fast. The danger of this with heavy clubs is you can get injured if you don't warm up properly first. So use them with caution.
For those that are interested, I've got a whole web site dedicated to building swing speed.
Jaacob
http://www.swingmangolf.com