Which type of Senate or House Committee is considered most important?

Answer 1

It depends on how you define "important." One could argue that they are all important.

However, the Rules Committees of each chamber are the most powerful because they set the agenda for which bills will be considered, when they will be considered, and under what terms they will be considered. Second to them would be the standing committees on specific subjects of importance to the nation, such as Judiciary and the Foreign Affairs Committees. Sub committees, Select Committees, and Joint Conference Committees may be most important for a narrow subject matter or bill and/or for a given time period.

Answer 2

House: Committee On Ways and Means
Senate: Senate Finance Committee.
Reason: The power to tax and spend is the power to compel.

Answer 3

I would say the finance or budget committees. They have the ability to manipulate every congressman or senator. Ask Robert Byrd (head of the senate finance committee) how he's convinced people to vote against their own bills for example. "The love of money is the root of all evil'. Just follow the money and all becomes clear.