I was wondering if it is at all possible to have one object in the viewport displayed as wireframe, while another is displayed as a solid?
Yes you can although I would think that seperate viewports are more friendly. What you do is to select the object that you want to be solid and then go to the display button and select display as solid. Other objects remain in wire-frame.
EDIT Whoops tried this on just one monitor, does not work as expected… sorry
Set the view to wireframe and set the object you want as solid as solid in its object properties.
The other way around: set the viewport shading to ‘Solid’, and the Display->Type (i.e. Maximum Draw Type) of the object you want as a wireframe to ‘Wire’.