should i...

I'm a newb so I can't offer technical advise on why an expensive bike is better than a cheap bike, but I would save up for a decent bike based on my experience this summer...

I did my first tri with about 10 friends this summer.  Half of us bought entry or just above entry level road bikes ($600-$1100 range) when we started training.  The other half used hybrids they owned or purchased cheaper bikes for $200-$300.  All but one of the guys on the hybrids/cheaper bikes went out and purchased a new road bike after our first tri.  The guy who didn't has stopped doing tris until he can buy a road bike. 

oh wow

what kind of bikes do you recomend? how is your bike treating you so far?

a cheap bike can be a good bike.  LOTS of people do races on mountain bikes and hybrids!  you can also look for used road bikes for a lot cheaper if you have your heart set on one. 

There are lots of USED "good bikes" out there that would be closer to your price range, but would not be something you would want to throw away after doing your first race and getting passed by a bunch of nicer bikes.

My first road bike was a used Bianchi with clip-on aero bars and Campagnolo components (gears, brakes). It was $300. It got me through about 5 years of this, until I had saved up for a tri bike. Which I also bought used for $2500.