newb needs some bike advice...

Well I have kinda been riding for awhile. I am more of a runner than a cyclist, but I do have an old roadbike that I got from a friend. It is very old and very outdated and in need of new tires. I want to get more acquainted with cycling. I am looking to train for long rides (I have a couple friends who every summer do a couple day ride across Nebraska). I also plan to compete in some triathlons and duathlons in the future. I need some advice as to what type of bike and what brands to look at. I dont wanna spend more than 800-900$ on my first bike and I wouldnt mind buying used. After doing a little bit of research, I see that they make triathlon specific bikes...what is the difference between those and regular touring bikes? Also, what else should I look into buying along with the bike. I already have a nice 60$ helmet that I wear and love. Any advice would be great, as Im sure you can tell Im really new to all this. Also, if any of you guys know a group in the Kansas City area that rides, that would help as well.
~Nick