Ok, Class C is what you got. Here is what I just posted in another thread:
Both ways have their pro/cons. I used to use my trailer for my little Class B. I almost got a Alumalite a few years back as that was a flat bed that could be used for anything when not used for the smart.
In the end my preference is the flat tow option. When the car isn't being towed there isn't any equipment laying around. At most you have a tow bar and cables (ours is always on the receiver on back of the motorhome with the rest in the basement of the MH).
Both ways are great. 6 one way - half dozen the other. We have a flat tow setup on my dad's smart which we tow behind a 34' Class A, driven it all over and it has done great. Each spring and fall I drive a 31' Class C (similar to your Greyhawk) 500 miles delivering a motorhome and smart for someone. As said before, you can barely tell it's there.
I used to do this with my budget rig. I paid $2000 for the motorhome and $500 for the trailer. Camping cheap.