Will whatever bill makes it out of the Senate still have to go through the House?
Yep. And then, assuming there are differing House and Senate bills (a certainty with this matter), those differences get worked out in conference, and the resulting compromise is voted on by the respective bodies.
Whatever comes out of THIS committee will have to be voted on by the whole Senate, after substantial (I am sure), debate...
Then, whatever bill the Senate DOES vote for will be sent to the House, where two groups of conferees will try to reconcile the two bills, whice are likely to be VERY DIFFERENT...
THAT is going to be the meeting I want to see---because that is where the real fireworks is going to occur, IMHO>
Yep, and if there is still disagreement between both the House and the Senate, both houses of Congress come together to work out a compromise.