Welcome to Permies. Great that you have your Farm!
Sod is agonizing to try to till, and tilling damp ground is not only difficult but potentially quite destructive to the structure, compacting the soil into dense clumps and creating an instant hardpan below your tiller tines.
I highly recommend cardboard instead of plastic. Unlike plastic, you can build up
compost and mulch on top of it, and it all makes soil in the end. Although it takes more work to separate the tape or staples from the cardboard, the soil microbes and worms love to live under cardboard. Since you are planning to plant squash, this works out well, since you can leave small spots open that you plant your squash plants and they will sprawl all over the cardboard, and squash loves to be mounded, which it seems would be beneficial on your plot. I recommend not tilling, but instead using that time and labor to build raised beds. Cover these with cardboard and plant squash in holes in the cardboard.
Dig out a pond, and or channel some of the water downhill to a chosen area, and make that area wetter, while drying the rest.
Start small and manage one smaller area intensively, so as to get ahead of the weeds.
You will have slugs, but I doubt, considering what you have wrote, that you are going to find a garden method that is not going to produce slugs on such land.
One thing to do to get rid of slugs is rotate chickens on half the land, and each year switch the chicken yard so that you are always gardening in a land that the chickens have eradicated the slug population during the previous year. Train the chickens to eat slugs by slicing slugs with a knife and tossing them to the chickens with other food scraps. Once they have a taste, they will seek them out.