When I first read your message, I missed the part about wanting a book about vegetable gardening.

I gardened in the Chicago area for many years, and my overall favorite book was The Well-Tended Perennial Garden: Planting and Pruning Techniques by Tracy DiSabato-Aust.

For vegetable gardening, I always used the "Victory Garden" by Crockett, or "The New Victory Garden" by Thompson. Alas, these books are only available as used books or for very high prices as new books.

I noticed a book recently published - Guide to Illinois Vegetable Gardening by James Fizzell. While I have not read the book myself, he is very well-regarded. He was the horticultural advisor to the University of Illinois Extension for 35 years. The University of Illinois Extension is a valuable resource. They had various locations across the state, (I've been gone for 4 years, not sure if they still have them.) Anyway, you could call for advice. If you had a particular plant or plant pest problem, you could visit the extension office to have the problem diagnosed and treatments suggested. I really miss the taste of homegrown Illinois tomatoes and also the taste of sweet-corn.
The soil around Chicago is very heavy soil, with lots of clay, so you need to add lots of peat moss or other organic matter to lighten it. However, it is also very rich soil.
Unfortunately, some of the best farmland in the country is now under concrete in the suburbs around Chicago.

I wish them luck in their new location. Where are they from? Perhaps the conditions are not as dissimilar. My top advice:
1 Peat moss and other organic matter
2 Water tubes around tomatoes in the spring (I think Burpee or Parks sells them)
3. Mulch the garden - weeds also grow very well in the rich soil
4 Old sheets or blankets for the fall - you can sometimes get 3 weeks more growth in the fall if you cover your tomatoes during an early frost. I think the average first frost date is October 15.