I recently rebuilt an 86 schwinn super sport frame with Campagnolo Athena (except shifters, record there) and a carbon fork. Including frame painting I'm in it less than a grand. It can be done.

OP, read a few guides about bikes and bike buying, or visit your lbs and chat with a sales rep. This time of year they're going to have the time to tell you whatever you want to know. I generally advise to skip the lowest entry point, since the next model is so much better, and 2k will get you a decent bike. Having said that its been my experience that a lot of people who get serious about riding find their ideal bike to be something other than their first bike, so I wouldn't tell you to spend up unless you know what you want already, and you don't. Until you spend about $1500 there's not a lot of difference from bike to bike anyway.