It IS important to have a stable foundation. A kneewall or stem wall is recommended to reach well below frost line where you are located. In northern areas that can be several feet. The purpose even in warmer climates is to prevent the heaving of the structure as the soil freezes and thaws making components buckle etc.
I have seen simple pole foundations heave even though they were planted at least a foot below frost line. Someone told me and haven't heard otherwise that a simple landscape cloth with a vapor barrier plastic around the perimeter would prevent the heaving action. But just so you know the risk.
If you do not want to put a cement wall in you can get away with putting up a wood perimeter for a base just make sure you replace the earth that the walls will sit on with grade "A" or "B" dirt because is will drain water better than the typical top soil the most yards are covered with and to help with the frost heaving you can use bails of hay to line the outside of the GH. I believe that 2 wide from the wall should be enough to reduce or stop any frost heaving.
so long as the crushed asphalt (aka rap) does not get compressed when hot in the summer it will stay pourous. it will be the same as a driveway no insulating properties at all. the frost line in your area is most likely just 2 feet deep at the most. the reason that I say use A or B grade of gravel is because of it's high draining, you want as much water to drain away or below the frost line to negate the heaving of the ground in winter. if you are going to raise the ground level of your yard then you have to remove the rap because it will compact and hold the water in your soil which you don't want.
It might help to know or understand how large of a structure you intend to build, how long would you want it to last as in a few years or several decades, and what kind of terrain will it be built upon. Assuming that commercial occupancy permits wouldn't be required, and the size is relatively small, you really might consider The Buried Post Footing on concrete alternatives. Here's a link to something I've seen in the way of pole barn construction in Colorado.
The Buried Post Footing
And here's a map showing the EXTREME case depth of frost line in the continental U.S.
Hope this helps.
I don't know much about foundations, though I did help build a pole barn here in Wisconsin a few years back and it's doing well.
The most important things to think about with designing your greenhouse is where you're going to store the sun's energy. Black-painted barrels filled with water against the back wall are a great way. You can also do one of those fan systems with plastic tubing buried in trenches to condense water at night and evaporate during the day for more energy storage.
It might be worth also considering how much energy, time and money you want to go into insulating your greenhouse and how much you want to spend insulating and air sealing your aquaponic system itself.