Here I am in Chicago (Evergreen Park) in 1963; I rode this bike to school and back 4 miles (1 mile each way & home for lunch) everyday. For a child growing up in the late 1950s/1960s, a bicycle meant freedom and a chance to explore your surrounding. One speed, balloon tires, probably 45 pounds. I was totally unaware that bicycle racing existed.
1994 Softride Power V; before carbon fiber was light. This was my first tri-bike; before this I used a Specialized road bike for a few races. Great bike but the carbon frame was a bit heavy. It eventually developed a crack and Softride replaced it with the frame below. Greg Welch won the Hawaiian Ironman on the Power V in 1994. This picture looks so dated now.
1999 Softride Rocket TT7, very aero. Softrides were still a bit heavy and they had a higher center of gravity due to the frame shape. The aero shape was better than anything else at the time and amazing on long downhills. I hit 51 mph descending Hospital Hill during a race in Clermont, FL. Weighing 175 pounds helps on downhills!
2005 Litespeed Tachyon; light & fast! I love this bike! The titanium frame with the carbon fork/seatpost does a fabulous job absorbing road shock and keeps the bike nice and light. Litespeed discontinued this model in 2008 and their aero shape tri-bike was a half pound heavier. I added a FSA Compact Crank (36/48) to give my old knees a break climbing hills.
You can do triathlons with any bike but having a tri/forward seatpost frame certainly helps to alleviate the "dead-legs" feeling I used to get off the bike on the run. The theory is that with the seat forward, you're utilizing a different set of leg muscles to pedal. You can find bike bargains on Craigslist or Ebay (if you know what to look for) or check out your Local Bike Shop's end of year sales. I got the Litespeed in 2006 when a LBS dropped Litespeed and cleared out their inventory. At the last race of 2009, I got a kick out of passing a 30 year old on a Cervelo P3 Carbon (disk wheel/aero helmet). Bicycling legend Eddy Merckx is quoted as saying, "You want to go faster? Pedal harder". You can buy speed on the bike but you still have to train to go fast. So which is the Right Bike? It's the one that feels right for you.