I basically have the same story as you: went to buy my first road bike, expecting to pay around $700, test rode a Giant OCR composite (carbon) frame and fell in love. I felt insane for spending $2400 on a bike. And now, six years later, I still think of that as the best $2400 I ever spent (especially since the bike went on sale 2 weeks later and they credited me $240, which I used to buy SIDI Dominators, some tools, and some other gear).
Seriously, if you can make it work with your budget, buy the bike you love.
2006 Giant OCRc
2011 Giant Escape City W
198? Univega Nuovo Sport 42/16 fixed gear conversion
1979 Peugeot 44/18 fixed gear conversion