My experience in this matter all comes from Kerbal Space Program... at which I'm admittedly not very good...

Whenever I try to build a rocket with a space plane component, I have to put bigger wings at the bottom of the rocket than the wings on the space plane at the top of the rocket.

Of course this has to do with the center of drag. Putting wings on the plane at the nose makes the rocket want to spin around in flight. But sticking big wings on the bottom of the rocket induces a whole bunch of drag that requires more fuel, gets into the whole rocket equation (more fuel to overcome more drags means you need every more fuel to lift the extra fuel you added and then more fuel to compensate for that fuel). You have to basically just use a plane fuselage with the smallest little control surface fins, hardly any wings.

I've wondered lately, is that why NASA was so interested in lifting bodies? Space planes that could ride at the top of the stack without needing a bunch of additional drag at the bottom of the rocket keep it stable?

Or was it just that someone thought that a plane with no wings was a cool idea?

I know part of the reason the Space Shuttle rode on the side of the stacks was so that the main engines would come back with the rest of the craft, but that orientation also puts the wings as far back as possible, which is at the very least a nice added benefit.