The ideal commuting bike is a light touring bike, and an ideal light touring bike can be had for much less than $3,000. $1,000 would do it. For that you could get a respectable 18-20 lbs cro-mo steel frame with quality components and add fenders, a rack and a Brooks saddle. A commuter bike can be fast, but it's not a racer. It needs to be all-weather with flat-resistant tires, a comfortable saddle, and room to carry a few things.