If you were a Democratic strategist, would you rather win the House or Senate? I understand the differences between the two in terms of responsibilities and size differences, but I'm still not understanding which would be more beneficial for the minority party to win. Your help is appreciated!

There is no one answer to this question that is clearly correct.  I can think of at least three answers that are equally valid.
First, you can argue that it does not matter which house of Congress the Democrats win if they are only going to win one house.  (And we don’t know who is going to be the president.)  If the Democrats only control one house and the presidency, they will not be able to push their agenda through Congress without Republican help anyway.   Therefore, it will not matter which house they control.  If the Democrats lose the presidency, they only need to control one house in order to obstruct whatever Trump tries to do while in office.  Either way, it does not matter which house they control.
Second, you can argue that it is better for them to control the House than the Senate.  The main reason for this is that a minority party in the Senate can obstruct anything it wants to under the current rules of the chamber.  As long as the Democrats stay united and have more than 40 senators, they can filibuster anything that the Republicans try to do.  In other words, they do not need to control the Senate in order to block the Republicans there.  In that case, they might as well control the House where the majority party has so much more power than it does in the Senate.
Finally, you can argue that the Democrats should prefer to control the Senate.  This is contingent on them being willing and able to change the rules governing the filibuster.  Some observers speculate that whichever party wins the Senate this election will try to do away with the filibuster because it has become such a powerful obstructive tool that nothing can get done in the Senate any longer.  If this happens, the Democrats would clearly want to control the Senate.  If they controlled the Senate and the filibuster no longer existed they could confirm any nominees put forward by a Clinton administration.  If they did not control the Senate and there was no filibuster, they would be unable to block any nominees that Trump named.  In this no-filibuster scenario, control of the Senate would be vitally important and Democrats would much prefer to control that chamber rather than the House.