So, I'm a cyclist.
I ride all kinds of bikes, makes, models, vintage etc. I ride Mountain, road and race from time to time.
Tri bikes are specialized/ geared towards the unique needs and demands of the dicipline. They have geometry, gearing and materials that have been refined and built with this single diciplines needs in mind. They are different from a road, mountain, cross or track bike.
Some people use these other styles of bikes for multiple disciplines. They do this because on a certain level a bicycle is a bicycle is a bicycle and they are not the best of the best where the differences of a true tri bike would make or break their placement in the upper echelons of the discipline.
You will find folks who use track bikes to race on the road as opposed to the velodrome, or mountain bikes to race cross, but at the elite levels, you will generally find only cross bikes for cross, road bikes for road, track bikes for track, tri bikes for tri and MTBs for 4x, downhill or cross country.
That said, if this is going to be a big part of your life and you are going to make a go of it, you need to go to a LBS (local bike shop) and be properly fitted to a tri bike. Only a handfull of dealers will know how to properly do this and your best bet is to ask other serious Tri competitors in your are where they go. You will need to go there in person.
Almost every major manufacturer of bicycles makes a bicycle for every discipline. Brand should not matter. Fit is what is going to matter. Trek, Giant, Specialized are generally the big three and they make as nice a bicycle as you could ever afford. There are other brands who make equally nice bicycles (truth be told they are usually made by the big three named above and in the same factory) and then there are custom builders who will build one just for you based on your body and needs. You can pay 500 to as high as youd ever like to go.
An entry level bike will start out between 5-700 dollars new. They will have standard and utilitarian parts. They will almost always be heavier. They will not shift as crisp, their wheels will not be as strong or stay as true as long as a mid-range bike. They will still have a very nice frame generaly speaking and will serve as a platform for replacements and upgrades to midrange parts as time and wear takes its toll. Midrange bikes will go from 800ish to just under 2 grand. Here you will get a strong, fairly light and durable machine and parts that are intended to last a while while providing lighter weight. Their parts are much more durable than the entry level bikes and the shifting is pretty close to on par with the high end machines. High end machines that you see the elite racing on are expensive and their parts and frames are very light and shift with precision. They are also throw away and are replaced every racing season. They do not buy these bikes but are sponsered by Trek or Specialized or whoever. You should not buy this kind of bike. You will break it and the parts will fail quickly relative to midrange bike. You will likely not be able to appreciate the refinements of the higher end bikes either. You will see people with money to burn who will buy the same Trek bike that Lance Armstrog races in the TDF. They will go on at length about their machine. You must remember that you are engine. Most of these racers would be better served by losing a few pounds from their bodies rather than spend two thousand extra dollars to save a few grams on the bicycle, but I digress.
You will always find an exception to what I've written above but for your purposes as a beginer, and until you learn more, you would do well to purchase a midrange machine. Tri bike s are always going to be more expensive simply due to supply and demand. I think youd do well to spend under 2000.00 new for a decent tri bike.
Get thee to a number of local bike shops, find one you like based on how they treat you and their level of knowledge and service of tri bikes. Try out as many models and brands as you can. Then get the one that fits the best. If it's a less expensive model then great, if it's little more expensive then so be it. Request a womens specific saddle and/or bike if you are woman. They will accomodate your deminsions better. Do not be afraid t buy a non-womans specific bike as long as it fits though. You can always adjust the cockpit such as reach, bar and saddle height, stem length, crank length, Q factor etc. and when being fitted to the bike, this is what they will do. Do request a womens specific saddle or saddle that is comfortable be swapped for the one on the bike if it is uncomfortable.
P.S. Don't be afraid to shop used but you must educate yourself as to what you are looking for. Until you gain in knowledge, especially working knowledge, you be better served to buy new.
Here are some links:http://www.bikeforums.net/showthread.php?t=436387
(read this first).http://www.bikeforums.net/
(they have a tri specific sub forum)http://www.roadbikereview.comhttp://www.slowtwitch.com/mainheadings/ ... kefit.html
if you are a woman: http://www.teamestrogen.com/content.ep?file=wsdBikes