I believe Silver at 538 once did an analysis of this, but really I do not believe there is a significant advantage for rising-star Representatives to waiting before they run for higher office. However, I'm pretty sure they universally have to win higher office first.
I think it depends. If you're going to run for an open Senate seat it may not necessarily help to have a lot of years in the House. If, however, you're going to challenge an incumbent, more years in the House may be helpful. It all depends on who you're running against, and where.
