pmurphy

I am not sure what material your greenhouse if made of but it is mostly likely polycarbonate panels, and I found that these greenhouses are not that heavy. Once set up they can easily be moved by one person (just clumsy) so you may not have to worry too much about settling; if anything, your 4x4's will probably weigh more.
I would simply dig a trench into the soil and lay your pressure treated 4x4 in this trench, making sure they are level at this time (once you get below the first couple of inches of soil is should firm up). You might even want to do a second level and bolt them together (I use 2 layers of landscape ties that were "overlapped" at the corners and then nailed together - usually cheaper than 4x4's and already treated). I then bolted the greenhouses onto the ties and placed a couple of layers of landscape fabric inside with rocks to help prevent weeds etc from growing.
I have found this worked for both of my greenhouses, one of which has been set up for almost 5 years now.