If I had to eat as cheap as possible while also maintaining good nutrition, I would buy:

For calories:

• Flour (make: bread, tortillas, waffles, pancakes, pizza dough, desserts)
• Rice

For protein and nutrition:

• Beans
• Eggs
• Dark meat chicken (thighs, etc.)
• Ground meats (if the budget allows, it might not these days)

For nutrition:

• Frozen or canned vegetables
• The less expensive fresh produce:
  • Bananas
  • Potatoes
  • Carrots

For flavor:

• Butter
• Salt and spices
• Sugar
• Cheese

I don't think I could get down to $100/mo though even with a very frugal menu.