The Speaker of the House is 2nd in line to the presidency.
The House initiates all fiscal bills.
The House shares the responsibility to declare War.
You are very right. Sometimes I think in the end the House is the most powerful branch, because of $$$.
The Speaker is only third in line, not second. The House is generally not involved in foreign diplomacy, that is the exclusive realm of the executive branch. The Senate gets involved in foreign matters by way of providing advice and consent for diplomats and other appointed positions and by approving treaties. The House, as you note, is only involved in declaring war. It doesn’t appear Obama is prepared to ask for a declaration of war against Iran. Israel remains to be seen.