Historically speaking, Chairman of House Ways and Means is one of the most powerful positions in Washington, maybe second only to the presidency itself.
This (Ways&Means) must be largely a powerful position, but without a public face. I cannot name who presently holds such a title now w/o googling it first. This relative anonymity may suit Paul better than a Presidency, as it is more bottom line, results oriented vs a Presidential role, which heavily relies on inflated egos and presumed charisma.