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.
Well, why would having more terms help you? It just gives your opponents more votes and stated positions and speeches to pour through. Maybe in years where Congress doesn't have record-low popularity, being an insider isn't as bad, but still, most of the advantages of being an insider come from institutional and fundraising support, not from the image of being an insider
In a partisan state like WA, in the current national climate especially, I see no real advantage to being a respected establishment Republican. Well, there's that one, but besides him.