One of the hardest things about getting into triathlons is the bike. If you're not used to biking, try to rent a bike or try out a friend's before committing. Is this something you're going to love? I had a crappy, commuter bike that I ride to and from lab. I love that damn bike. I tried going around the park more and riding out on that for awhile. I loved it, but wanted something that was a little faster. My bike felt like a mule. I wanted a Thoroughbred.
I checked out all the bike shops, read the bicycling magazines, read the chat and message boards about bikes, and tried out a bunch of bikes. I decided on a road bike since it would be very suitable for triathlons but also for general biking as well. They make triathlon-specific bikes, but they are more expensive, less comfortable, and only should be awarded to the more committed triathlete (in my opinion). I decided if I got serious, I could always take my bike to the bike shop and get it fitted for aerobars (I don't like the simple clip-ons b/c you should shorten the top tube and adjust the stem for the different position. Your back will thank you.)
They have all sorts of road bikes. It was overwhelming. Touring, racing, etc. My price range was about $1000. I wanted the bike with the best components (gears, shifters, etc.). A lot of bikes can be very similar since they are often made by the same manufacturers. Raleigh, Specialized, Pacific--all made by the same people. I eliminated Trek and Cannondale b/c I was paying for the label and getting lesser qualilty components for my price range. Plus, I didn't find them all that comfortable. I really liked the Specialized Allez (my father owns this bike now). I also loved Bianchi--what a smooth ride. But it was more of a touring bike, and I feared the steel frame would weigh me down. But, oh, I may lust after that in the future for a century ride. Then I found Felt. Not as well known but has a good frame and good components. I liked the feel of it a bit better and decided on this bike for my first road bike. I've been very happy with it.
My advice is 1) find a good bike shop with knowledgeable, friendly, helpful people. They shouldn't intimidate you and should be excited to get you involved with biking. The staff should all be bicyclists too. They should offer free tune-ups of bikes you purchase from them and should stand behind their products. Your local bike shop will be your best friend. I bug my local bike shop all the time. They're great.
2) Try the bike you're going to buy. Try it a few times. Compare it to several others. Buy the bike that is most comfortable for you.
3) Have the bike professionally fitted to your body. The bike shop should do this free of charge (see #1).
4) See if your area has a bike club that sponsors fun rides. This is a great way to meet other bicyclists and go on rides where you don't have to worry about where you're going or break-downs.
5) Be safe. Cars aren't always respectful of bicyclists. Wear a helmet. Bring a water bottle and a repair kit. Know how to change a flat. Always follow the rules of the road. You are vehicle on the road and should follow the same laws. You can get cited for running reds or stop signs.
Hope this helps! Have fun!