Congress does seem like an intuitive choice to decide the president. After all, it's an elected body, the relative weight of each state's influence has been decided already, and the congressmen would surely be well aquanted with anyone of such "continental stature" as to run for president. However, if congress elected the president everyone would know who the electors were for at least two years before the election. The framers were concerned that this would leave the members of congress open to bribery or falling under the unfair influence by factions or nefarious meddling foreign powers. The advantages of having the congress elect the president are impossible to ignore however, so what are we to do? Well, we elect a shadow congress every election in the form of the electoral college. The electoral college is weighted exactly the same as congress (each state gets at least two votes, and then as many votes as they have members in the House of Representatives), with the exception that Washington D.C. also gets three electors as a result of the 23rd amendment despite the district having no congressional representation.

I'm at work right now (tsk tsk), but I'll properly source once I'm home.