Enjoy your first year because no chemicals essentially means no weed control and after weeds go to seed and get buried in subsequent cultivation you will have a compounding weed problem that will be out of control in one year. Take one weed seed today and double it every day for 30 days and you will have a million seeds. Some plants (marestail) produce 200,000 seeds each and some weeds (giant ragweed) can live 70 years in dormancy. You do the math.
Better idea is to concentrate your crops to simplify production problems and rethink herbicides. A few acres of sweet corn--maybe in two or three batches will stagger maturities and one squash variety will be all you can handle. Before you choose the squash, ask the Extension Agent to see what others around there have had success or failure with. My guess for Nebraska is that you will need some sort of powdery mildew protection and some sort of squash bug protection. Find a plant with some natural resistance and you'll have a leg up. Sweet corn should be no problem for you, especially so if you plant the seed deep enough and maybe have someone spray a pre-emergent to keep the weeds down. "Organic" bug control often involves chemicals far more dangerous than chemical means. Both of them kill bugs, although "natural" is more romantic.
We used to plant a lot of sweet corn and 8 acres of squash/ pumpkins and weed control for us was a full-time job. We tried to never let even one weed plant go to seed. If it does, things start compounded immediately. As it is the wind will bring in grass and other seeds to make life difficult.
We used to use "Post" as a grass killer over squash and pumpkins and it did a great job. We used a rototiller to cross-check cultivate for weeds and it worked fine. For corn we used to spray Roundup before planting to control emerged weeds, planted no-till after that and then would spray 2,4-D and cultivate in the row for weed control. It worked very well.
Since you have several tractors, I would set up one with a planter, one with a small sprayer (2,4-D for the corn) and one with a cultivator. That setup will really help with success potential. If you are ideologically opposed to any chemicals for weed or pest control better idea is to save the money and buy at the supermarket. Use the intended money for some other purpose or maybe another tractor. Just my personal opinion from already having done what you are thinking of doing. Keep us posted--pictures always welcome-- and enjoy the effort.
